[1] L., Accardi, F., Fagnola (eds.). Quantum interacting particle systems. In: Proc. Volterra-CIRM Int. School, Trento, 2000, QP-PQ: Quantum Probability and White Noise Analysis, vol. 14, World Scientific, 2002.

[2] S., Albeverio, A., Hilbert and V., Kolokoltsov. Sur le comportement asymptotique du noyau associé à une diffusion dégénéré. C.R. Math. Rep. Acad. Sci. Canada 22:4 (2000), 151–159.Google Scholar

[3] S., Albeverio, B., Rüdiger. Stochastic integrals and the Lévy-Ito decomposition theorem on separable Banach spaces. Stoch. Anal. Appl. 23:2 (2005), 217–253.Google Scholar

[4] D.J., Aldous. Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists. Bernoulli 5:1 (1999), 3–48.Google Scholar

[5] H., Amann. Coagulation-fragmentation processes. Arch. Ration. Mech. Anal. 151 (2000), 339–366.Google Scholar

[6] W. J., Anderson. Continuous-Time Markov Chains. Probability and its Applications. Springer Series in Statistics. Springer, 1991.

[7] D., Applebaum. Probability and Information.Cambridge University Press, 1996.

[8] D., Applebaum. Lévy Processes and Stochastic Calculus. Cambridge Studies in Advanced Mathematics, vol. 93. Cambridge University Press, 2004.

[9] O., Arino, R., Rudnicki. Phytoplankton dynamics. Comptes Rendus Biol. 327 (2004), 961–969.Google Scholar

[10] L., Arkeryd. On the Boltzmann equation. Parts I and II. Arch. Ration. Mech. Anal. 45 (1972), 1–35.Google Scholar

[11] L., Arkeryd. L∞ Estimates for the spatially-homogeneous Boltzmann equation. J. Stat. Phys. 31:2 (1983), 347–361.Google Scholar

[12] A. A., Arseniev. Lektsii o kineticheskikh uravneniyakh (in Russian) (Lectures on kinetic equations). Nauka, Moscow, 1992.

[13] A. A., Arseniev, O. E., Buryak. On a connection between the solution of the Boltzmann equation and the solution of the Landau-Fokker-Planck equation (in Russian). Mat. Sb. 181:4 (1990), 435-446; English translation in Math. USSR Sb. 69:2 (1991), 465–478.Google Scholar

[14] I., Bailleul. Sensitivity for Smoluchovski equation. Preprint 2009. http://www. statslab.cam.ac.uk/ismael/files/Sensitivity.pdf.

[15] A., Bain, D., Crisan. Fundamentals of Stochastic Filtering. Stochastic Modelling and Applied Probability, vol. 60. Springer, 2009.

[16] R., Balescu. Statistical Dynamics. Matter out of Equilibrium.Imperial College Press, 1997.

[17] J. M., Ball, J., Carr. The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation. J. Stat. Phys. 61 (1990), 203–234.Google Scholar

[18] R. F., Bass. Uniqueness in law for pure jump type Markov processes. Prob. Theory Relat. Fields 79 (1988), 271–287.Google Scholar

[19] R. F., Bass, Z.-Q., Chen. Systems of equations driven by stable processes. Prob. Theory Relat. Fields 134 (2006), 175–214.Google Scholar

[20] P., Becker-Kern, M. M., Meerschaert, H.-P., Scheffler. Limit theorems for coupled continuous time random walks. Ann. Prob. 32:1B (2004), 730–756.Google Scholar

[21] V. P., Belavkin. Quantum branching processes and nonlinear dynamics of multi-quantum systems (in Russian). Dokl. Acad. Nauk SSSR 301:6 (1988), 1348–1352.Google Scholar

[22] V. P., Belavkin. Multiquantum systems and point processes I. Rep. Math. Phys. 28 (1989), 57–90.Google Scholar

[23] V. P., Belavkin, V. N., Kolokoltsov. Stochastic evolutions as boundary value problems. In: Infinite Dimensional Analysis and Quantum Probability, RIMS Kokyuroku 1227 (2001), 83–95.

[24] V. P., Belavkin, V. N., Kolokoltsov. Stochastic evolution as interaction representation of a boundary value problem for Dirac type equation. Inf. Dim. Anal., Quantum Prob. Relat. Fields 5:1 (2002), 61–92.Google Scholar

[25] V. P., Belavkin, V. N., Kolokoltsov. On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. Roy. Soc. London A 459 (2003), 727–748.Google Scholar

[26] V. P., Belavkin, V. P., Maslov. Uniformization method in the theory of nonlinear hamiltonian systems of Vlasov and Hartree type (in Russian). Teoret. i Matem. Fizika 33:1 (1977), 17–31. English translation in Theor. Math. Phys. 43:3 (1977), 852–862.Google Scholar

[27] R. E., Bellman. Dynamic Programming. Princeton University Press and Oxford University Press, 1957.

[28] G. Ben, Arous. Developpement asymptotique du noyau de la chaleur sur la diagonale. Ann. Inst. Fourier 39:1 (1989), 73–99.Google Scholar

[29] A., Bendikov. Asymptotic formulas for symmetric stable semigroups. Exp. Math. 12 (1994), 381–384.Google Scholar

[30] V., Bening, V., Korolev, T., Suchorukova, G., Gusarov, V., Saenko, V., Kolokoltsov. Fractionally stable distributions. In: V., Korolev, N., Skvortsova (eds.), Stochastic Models ofPlasma Turbulence (in Russian), Moscow State University, 2003, pp. 291-360. English translation in V. Korolev, N. Skvortsova (eds.), Stochastic Models ofStructural Plasma Turbulence, VSP, 2006, pp. 175-244.

[31] V., Bening, V., Korolev, V., Kolokoltsov. Limit theorems for continuous-time random walks in the double array limit scheme. J. Math. Sci. (NY) 138:1 (2006), 5348–5365.Google Scholar

[32] J., Bennett, J.-L., Wu. Stochastic differential equations with polar-decomposed Levy measures and applications to stochastic optimization. Fron. Math. China 2:4 (2007), 539–558.Google Scholar

[33] J., Bertoin. Lévy Processes. Cambridge Tracts in Mathematics, vol. 121, Cambridge University Press, 1996.

[34] J., Bertoin. Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics, vol. 102, Cambridge University Press, 2006.

[35] K., Bichteler. Stochastic Integration with Jumps. Encyclopedia of Mathematics and Applications, Cambridge University Press, 2002.

[36] K., Bichteler, J.-B., Gravereaux, J., Jacod. Malliavin Calculus for Processes with Jumps. Stochastic Monographs, vol. 2, Gordon and Breach, 1987.

[37] P., Biler, L., Brandolese. Global existence versus blow up for some models of interacting particles. Colloq. Math. 106:2 (2006), 293–303.Google Scholar

[38] P., Billingsley. Convergence of Probability Measures. Wiley, 1968.

[39] H., Bliedtner, W., Hansen. Potential Theory – An Analytic Approach to Balayage. Universitext, Springer, 1986.

[40] R. M., Blumenthal, R. K., Getoor. Some theorems on stable processes. Trans. Amer. Math. Soc. 95 (1960), 263–273.Google Scholar

[41] A. V., Bobylev. The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Sov. Sci. Rev. C, Math. Phys. Rev. 7 (1988), 111–233.Google Scholar

[42] N.N., Bogolyubov. Problems of the Dynamic Theory in Statistical Physics. Moscow, 1946 (in Russian).

[43] J.-M., Bony, Ph., Courrège, P., Priouret. Semi-groupes de Feller sur une variété a bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum. Ann. Inst. Fourier, Grenoble 18:2 (1968), 369–521.Google Scholar

[44] Yu. D., Burago, V. A., Zalgaller. Geometric Inequalities. Springer, 1988.

[45] T., Carleman. Problèmes mathématique dans la théorie cinétique des gaz. Almquist and Wiksells, 1957.

[46] R. A., Carmona, D., Nualart. Nonlinear Stochastic Integrators, Equations and Flows. Stochatic Monographs, vol. 6, Gordon and Breach, 1990.

[47] C., Cercognani, R., Illner, M., Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, 1994.

[48] A. M., Chebotarev. A priori estimates for quantum dynamic semigroups (in Russian). Teoret. Mat. Fiz 134:2 (2003), 185-190; English translation in Theor. Math. Phys. 134:2 (2003), 160–165.Google Scholar

[49] A. M., Chebotarev, F., Fagnola. Sufficient conditions for conservativity of minimal quantum dynamic semigroups. J. Funct. Anal. 118 (1993), 131–153.Google Scholar

[50] A. M., Chebotarev, F., Fagnola. Sufficient conditions for conservativity of minimal quantum dynamic semigroups. J. Funct. Anal. 153 (1998), 382–104.Google Scholar

[51] J. F., Collet, F., Poupaud. Existence of solutions to coagulation-fragmentation systems with diffusion. Transport Theory Statist. Phys. 25 (1996), 503–513.Google Scholar

[52] Ph., Courrège. Sur la forme integro-différentiélle du générateur infinitésimal d'un semi-groupe de Feller sur une variété. In: Sém. Théorie du Potentiel, 1965–1966. Exposé 3.

[53] F. P., da Costa, H. J., Roessel, J. A. D., Wattis. Long-time behaviour and self-similarity in a coagulation equation with input of monomers. Markov Proc. Relat. Fields 12 (2006), 367–398.Google Scholar

[54] D., Crisan, J., Xiong. Approximate McKean-Vlasov representations for a class of SPDEs. To appear in Stochastics.

[55] R. F., Curtain. Riccati equations for stable well-posed linear systems: the generic case. SIAMJ. Control Optim. 42: 5 (2003), 1681-1702 (electronic).Google Scholar

[56] E. B., Davies. Quantum Theory of Open Systems. Academic Press, 1976.

[57] E. B., Davies. Heat Kernels and Spectral Theory. Cambridge University Press, 1992.

[58] D., Dawson. Critical dynamics and fluctuations for a mean-field model of cooperative behavior. J. Stat. Phys. 31: 1 (1983), 29–85.Google Scholar

[59] D., Dawson. Measure-valued Markov processes. In: P. L., Hennequin (ed.), Proc. Ecole d'Eté de probabilités de Saint-Flour XXI, 1991. Springer Lecture Notes in Mathematics, vol. 1541, 1993, pp. 1-260.

[60] D., Dawsonet al.Generalized Mehler semigroups and catalytic branching processes with immigration. Potential Anal. 21:1 (2004), 75–97.Google Scholar

[61] A., de Masi, E., Presutti. Mathematical Methods for Hydrodynamic Limits. Springer, 1991.

[62] M., Deaconu, N., Fournier, E., Tanré. A pure jump Markov process associated with Smoluchovski's coagulation equation. Ann. Prob. 30:4 (2002), 1763–1796.Google Scholar

[63] M., Deaconu, N., Fournier, E., Tanré. Rate of convergence of a stochastic particle system for the Smoluchovski coagulation equation. Methodol. Comput. Appl. Prob. 5:2 (2003), 131–158.Google Scholar

[64] P., Del Moral. Feynman-Kac Formulae. Genealogical and Interacting particle Systems with Applications. Probability and its Application. Springer, 2004.

[65] L., Desvillettes, C., Villani. On the spatially homogeneous Landau equation for hard potentials. Part I. Comm. Partial Diff. Eq. 25 (2000), 179–259.Google Scholar

[66] S., Dharmadhikari, K., Joag-Dev. Unimodality, Convexity, and Applications. Academic Press, 1988.

[67] B., Driver, M., Röckner. Constructions of diffusions on path spaces and loop spaces of compact riemannian manifolds. C.R. Acad. Sci. Paris, Ser. I 320 (1995), 1249–1254.Google Scholar

[68] P. B., Dubovskii, I. W., Stewart. Existence, uniqueness and mass conservation for the coagulation-fragmentation equation. Math. Meth. Appl. Sci. 19 (1996), 571–591.Google Scholar

[69] E. B., Dynkin. Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations. University Lecture Series, vol. 34, American Mathematical Society, 2004.

[70] A., Eibeck, W., Wagner. Stochastic particle approximation to Smoluchovski's coagulation equation. Ann. Appl. Prob. 11:4 (2001), 1137–1165.Google Scholar

[71] T., Elmroth. Global boundedness of moments of solutions of the Boltzmann equation for forces of inifinite range. Arch. Ration. Mech. Anal. 82 (1983), 1–12.Google Scholar

[72] F. O., Ernst, S.E., Protsinis. Self-preservation and gelation during turbulance induced coagulation. J. Aerosol Sci. 37:2 (2006), 123–142.Google Scholar

[73] A. M., Etheridge. An Introduction to Superprocesses. University Lecture Series, vol. 20, American Mathematical Society, 2000.

[74] S.N., Ethier, Th. G., Kurtz. Markov Processes – Characterization and Convergence. Wiley Series in Probability and Mathematical Statistics, Wiley, 1986.

[75] K., Evans, N., Jacob. Feller semigroups obtained by variable order subordination. Rev. Mat. Comput. 20:2 (2007), 293–307.Google Scholar

[76] W., Feller. An Introduction to Probability. Theory and Applications, second edition, vol. 2. John Wiley and Sons, 1971.

[77] N., Fournier, Ph., Laurencot. Local properties of self-similar solutions to Smoluchowski's coagulation equation with sum kernels. Proc. Roy. Soc. Edinburgh. A 136 :3 (2006), 485–508.Google Scholar

[78] M., Freidlin. Functional Integration and Partial Differential Equations. Princeton University Press, 1985.

[79] T.D., Frank. Nonlinear Markov processes. Phys. Lett. A 372:25 (2008), 4553–4555.Google Scholar

[80] B., Franke. The scaling limit behavior of periodic stable-like processes. Bernoulli 21:3 (2006), 551–570.Google Scholar

[81] M., Fukushima, Y., Oshima, M., Takeda. Dirichlet Forms and Symmetric Markov Processes. de Gruyter, 1994.

[82] J., Gärtner. On the McKean-Vlasov limit for interacting diffusions. Math. Nachri. 137 (1988), 197–248.Google Scholar

[83] E., Giné, J. A., Wellner. Uniform convergence in some limit theorem for multiple particle systems. Stochastic Proc. Appl. 72 (1997), 47–72.Google Scholar

[84] H., Gintis. Game Theory Evolving. Princeton University Press, 2000.

[85] T., Goudon. Sur l'equation de Boltzmann homogène et sa relation avec l'equation de Landau-Fokker-Planck. C.R. Acad. Sci. Paris 324, 265-270.

[86] S., Graf, R. D., Mauldin. A classification of disintegrations of measures. In: Measures and Measurable Dynamics. Contemporary Mathematics, vol. 94, American Mathematical Society, 1989, 147-158.

[87] G., Graham, S., Méléard. Chaos hypothesis for a system interacting through shared resources. Prob. Theory Relat. Fields 100 (1994), 157–173.Google Scholar

[88] G., Graham, S., Méléard. Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Prob. 25:1 (1997), 115–132.Google Scholar

[89] H., Guérin. Existence and regularity of a weak function-solution for some Landau equations with a stochastic approach. Stoch. Proc. Appl. 101 (2002), 303–325.Google Scholar

[90] H., Guérin. Landau equation for some soft potentials through a probabilistic approach. Ann. Appl. Prob. 13:2 (2003), 515–539.Google Scholar

[91] H., Guérin, S., Méléard, E., Nualart. Estimates for the density of a nonlinear Landau process. J. Funct. Anal. 238 (2006), 649–677.Google Scholar

[92] T., Gustafsson. Lp -properties for the nonlinear spatially homogeneous Boltzmann equation. Arch. Ration. Mech. Anal. 92 (1986), 23–57.Google Scholar

[93] T., Gustafsson. Global Lp-properties for the spatially homogeneous Boltzmann equation. Arch. Ration. Mech. Anal. 103 (1988), 1–38.Google Scholar

[94] O., Hernandez-Lerma. Lectures on Continuous-Time Markov Control Processes. Aportaciones Matematicas, vol. 3, Sociedad Matematica Mexicana, Mexico, 1994.

[95] O., Hernandez-Lerma, J. B., Lasserre, J., Bernard. Discrete-Time Markov Control Processes. Basic Optimality Criteria. Applications of Mathematics, vol. 30. Springer, 1996.

[96] J., Hofbauer, K., Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998.

[97] W., Hoh. The martingale problem for a class of pseudo differential operators. Math. Ann. 300 (1994), 121–147.Google Scholar

[98] W., Hoh, N., Jacob. On the Dirichlet problem for pseudodifferential operators generating Feller semigroups. J. Funct. Anal. 137:1 (1996), 19–48.Google Scholar

[99] A. S., Holevo. Conditionally positive definite functions in quantum probability (in Russian). In: Itogi Nauki i Tekniki. Modern Problems of Mathematics, vol. 36, 1990, pp. 103-148.

[100] M., Huang, R.P., Malhame, P.E., Caines. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6:3 (2006), 221–251.Google Scholar

[101] T. J. R., Hughes, T., Kato, J.E., Marsden. Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Arch. Ration. Mech. Anal. 63:3 (1976), 273–294.Google Scholar

[102] S., Ito, Diffusion equations. Translations of Mathematical Monographs, vol. 114. American Mathematical Society, 1992.

[103] N., Jacob. Pseudo-Differential Operators and Markov Processes, vols. I, II, III. Imperial College London Press, 2001, 2002, 2005.

[104] N., Jacob, R. L., Schilling. Lévy-type processes and pseudodifferential operators. In: O. E., Barndorff-Nielsenet al. (eds), Lévy Processes, Theory and Applications, Birkhäuser, 2001, pp. 139-168.

[105] N., Jacobet al.Non-local (semi-)Dirichlet forms generated by pseudo differential operators. In: Z. M., Maet al. (eds.), Dirichlet Forms and Stochastic Processes, Proc. Int. Conf. Beijing 1993, de Gruyter, 1995, pp. 223-233.

[106] J., Jacod, Ph., Protter. Probability Essentials. Springer, 2004.

[107] J., Jacod, A. N., Shiryaev. Limit Theorems for Stochastic Processes. Springer, 1987. Second edition, 2003.

[108] A., Jakubowski. On the Skorohod topology. Ann. Inst. H. Poincaré B22 (1986), 263–285.Google Scholar

[109] I., Jeon. Existence of gelling solutions for coagulation-fragmentation equations. Commun. Math. Phys. 194 (1998), 541–567.Google Scholar

[110] E., Joergensen. Construction of the Brownian motion and the Orstein-Uhlenbeck Process in a Riemannian manifold. Z. Wahrsch. verw. Gebiete 44 (1978), 71–87.Google Scholar

[111] A., Joffe, M., Métivier. Weak convergence of sequence of semimartingales with applications to multitype branching processes. Adv. Appl. Prob. 18 (1986), 20–65.Google Scholar

[112] J., Jost. Nonlinear Dirichlet forms. In: New Directions in Dirichlet Forms, American Mathematical Society/IP Studies in Advanced Mathematics, vol. 8, American Mathematical Society, 1998, pp. 1-47.

[113] M., Kac. Probability and Related Topics in Physical Science. Interscience, 1959.

[114] O., Kallenberg. Foundations of Modern Probability, second edition. Springer, 2002.

[115] I., Karatzas, S., Shreve. Brownian Motion and Stochastic Calculus. Springer, 1998.

[116] T., Kato. Quasi-linear equations of evolution, with applications to partial differential equations. In: Spectral Theory and Differential Equations, Proc. Symp. Dundee, 1974, Lecture Notes in Mathematics, vol. 448, Springer, 1975, pp. 25-70.

[117] T., Kazumi. Le processes d'Ornstein-Uhlenbeck sur l'espace des chemins et le probleme des martingales. J. Funct. Anal. 144 (1997), 20–45.Google Scholar

[118] A., Khinchine. Sur la crosissance locale des prosessus stochastiques homogènes à acroissements indépendants. Isvestia Akad. Nauk SSSR, Ser. Math. (1939), 487–508.

[119] K., Kikuchi, A., Negoro. On Markov processes generated by pseudodifferential operator of variable order. Osaka J. Math. 34 (1997), 319–335.Google Scholar

[120] C., Kipnis, C., Landim. Scaling Limits of Interacting Particle Systems. Grundlehren der Mathematischen Wissenschaften, vol. 320, Springer, 1999.

[121] A. N., Kochubei. Parabolic pseudo-differentiable equations, supersingular integrals and Markov processes (in Russian). Izvestia Akad. Nauk, Ser. Matem. 52:5 (1988), 909–934. English translation in Math. USSR Izv. 33:2 (1989), 233–259.Google Scholar

[122] A., Kolodko, K., Sabelfeld, W., Wagner. A stochastic method for solving Smolu-chowski's coagulation equation. Math. Comput. Simulation 49 (1999), 57–79.Google Scholar

[123] V. N., Kolokoltsov. On linear, additive, and homogeneous operators in idempo-tent analysis. In: V. P., Maslov and S. N., Samborski: (eds.), Idempotent Analysis, Advances in Soviet Mathematics, vol. 13, 1992, pp. 87-101.

[124] V. N., Kolokoltsov. Semiclassical Analysis for Diffusions and Stochastic Processes. Springer Lecture Notes in Mathematics, vol. 1724, Springer, 2000.

[125] V. N., Kolokoltsov. Symmetric stable laws and stable-like jump-diffusions. Proc. London Math. Soc. 3 80 (2000), 725–768.Google Scholar

[126] V. N., Kolokoltsov. Small diffusion and fast dying out asymptotics for super-processes as non-Hamiltonian quasi-classics for evolution equations. Electronic J. Prob., http://www.math.washington.edu/ ejpecp/ 6 (2001), paper 21.

[127] V. N., Kolokoltsov. Measure-valued limits of interacting particle systems with k-nary interactions I. Prob. Theory Relat. Fields 126 (2003), 364–394.Google Scholar

[128] V. N., Kolokoltsov. On extension of mollified Boltzmann and Smoluchovski equations to particle systems with a k-nary interaction. Russian J. Math. Phys. 10 3 (2003), 268–295.Google Scholar

[129] V. N., Kolokoltsov. Measure-valued limits of interacting particle systems with k-nary interactions II. Stoch. Stoch. Rep. 76 1 (2004), 45–58.Google Scholar

[130] V. N., Kolokoltsov. On Markov processes with decomposable pseudo-differential generators. Stoch. Stoch. Rep. 76 1 (2004), 1–44.Google Scholar

[131] V. N., Kolokoltsov. Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles. J. Stati. Phys. 115: 5/6 (2004), 1621–1653.Google Scholar

[132] V. N., Kolokoltsov. Kinetic equations for the pure jump models of k-nary interacting particle systems. Markov Proc. Relat. Fields 12 (2006), 95–138.Google Scholar

[133] V. N., Kolokoltsov. On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. AdvancedStud. Contemp. Math. 12 (2006), 9–38.Google Scholar

[134] V. N., Kolokoltsov. Nonlinear Markov semigroups and interacting Lévy type processes. J. Stat. Phys. 126:3 (2007), 585–642.Google Scholar

[135] V. N., Kolokoltsov. Generalized continuous-time random walks (CTRW), subordination by hitting times and fractional dynamics. arXiv:0706.1928v1[math.PR] 2007. Probab. Theory Appl. 53:4 (2009), 594–609.Google Scholar

[136] V. N., Kolokoltsov. The central limit theorem for the Smoluchovski coagulation model. arXiv:0708.0329v1[math.PR] 2007. Prob. Theory Relat. Fields 146:1 (2010), 87. Published online, http://dx.doi.org/10.1007/s00440-008-0186-2.CrossRefGoogle Scholar

[137] V.N., Kolokoltsov. The Lévy-Khintchine type operators with variable Lips-chitz continuous coefficients generate linear or nonlinear Markov processes and semigroupos. To appear in Prob. Theory. Relat. Fields.

[138] V.N., Kolokoltsov, V., Korolev, V., Uchaikin. Fractional stable distributions. J. Math. Sci. (N.Y.) 105:6 (2001), 2570–2577.Google Scholar

[139] V. N., Kolokoltsov, O. A., Malafeyev. Introduction to the Analysis of Many Agent Systems of Competition and Cooperation (Game Theory for All). St Petersburg University Press, 2008 (in Russian).

[140] V. N., Kolokoltsov, O. A., Malafeyev. Understanding Game Theory. World Scientific, 2010.

[141] V.N., Kolokoltsov, V.P., Maslov. Idempotent Analysis and its Application to Optimal Control. Moscow, Nauka, 1994 (in Russian).

[142] V. N., Kolokoltsov, V. P., Maslov. Idempotent Analysis and its Applications. Kluwer, 1997.

[143] V.N., Kolokoltsov, R.L., Schilling, A.E., Tyukov. Transience and non-explosion of certain stochastic newtonian systems. Electronic J. Prob. 7 (2002), paper no. 19.Google Scholar

[144] T., Komatsu. On the martingale problem for generators of stable processes with perturbations. Osaka J. Math. 21 (1984), 113–132.Google Scholar

[145] V. Yu., Korolev, V. E., Bening, S. Ya., Shorgin. Mathematical Foundation of Risk Theory. Moscow, Fismatlit, 2007 (in Russian).

[146] V., Korolevet al.Some methods of the analysis of time characteristics of catastrophes in nonhomogeneous flows of extremal events. In: I.A., Sokolov (ed.), Sistemi i Sredstva Informatiki. Matematicheskie Modeli v Informacionnich Technologiach, Moscow, RAN, 2006, pp. 5-23 (in Russian).

[147] M., Kostoglou, A.J., Karabelas. A study of the nonlinear breakage equations: analytical and asymptotic solutions. J. Phys. A 33 (2000), 1221–1232.Google Scholar

[148] M., Kotulski. Asymptotic distribution of continuous-time random walks: a probabilistic approach. J. Stat. Phys. 81:3/4 (1995), 777–792.Google Scholar

[149] M., Kraft, A., Vikhansky. A Monte Carlo method for identification and sensitivity analysis of coagulation processes. J. Comput. Phys. 200 (2004), 50–59.Google Scholar

[150] H., Kunita. Stochastic Flows and Stochastic Differential Equations. Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, 1990.

[151] T. G., Kurtz, J., Xiong. Particle representations for a class of nonlinear SPDEs. Stochastic Proc. Appl. 83:1 (1999), 103–126.Google Scholar

[152] T. G., Kurtz, J., Xiong. Numerical solutions for a class of SPDEs with application to filtering. In: Stochastics in Finite and Infinite Dimensions, Trends in Mathematics, Birkhäuser, 2001, pp. 233-258.

[153] A. E., Kyprianou. Introductory Lectures on Fluctuations of Lévy Processes with Applications. Universitext, Springer, 2006.

[154] M., Lachowicz. Stochastic semigroups and coagulation equations. Ukrainian Math. J. 57:6 (2005), 913–922.Google Scholar

[155] M., Lachowicz, Ph., Laurencot, D., Wrzosek. On the Oort-Hulst-Savronov coagulation equation and its relation to the Smoluchowski equation. SIAM J. Math. Anal. 34 (2003), 1399–1421.Google Scholar

[156] P., Laurencot, S., Mischler. The continuous coagulation-fragmentation equations with diffusion. Arch. Ration. Mech. Anal. 162 (2002), 45–99.Google Scholar

[157] P., Laurencot, D., Wrzosek. The discrete coagulation equations with collisional breakage. J. Stat. Phys. 104: 1/2 (2001), 193–220.Google Scholar

[158] R., Leandre. Uniform upper bounds for hypoelliptic kernels with drift. J. Math. Kyoto University 34:2 (1994), 263–271.Google Scholar

[159] J. L., Lebowitz, E.W., Montroll (eds.). Non-Equilibrium Phenomena I: The Boltzmann Equation. Studies in Statistical Mechanics, vol. X, North-Holland, 1983.

[160] M. A., Leontovich. Main equations of the kinetic theory from the point of view of random processes (in Russian). J. Exp. Theoret. Phys. 5 (1935), 211–231.Google Scholar

[161] P., Lescot, M., Roeckner. Perturbations of generalized Mehler semigroups and applications to stochastic heat equation with Levy noise and singular drift. Potential Anal. 20:4 (2004), 317–344.Google Scholar

[162] T., Liggett. Interacting Particle Systems. Reprint of the 1985 original. Classics in Mathematics, Springer, 2005.

[163] G., Lindblad. On the Generators of quantum dynamic semigroups. Commun. Math. Phys. 48 (1976), 119–130.Google Scholar

[164] X., Lu, B., Wennberg. Solutions with increasing energy for the spatially homogeneous Boltzmann equation. Nonlinear Anal. Real World Appl. 3 (2002), 243–258.Google Scholar

[165] A. A., Lushnikov. Some new aspects of coagulation theory. Izv. Akad. Nauk SSSR, Ser. Fiz. Atmosfer. i Okeana 14:10 (1978), 738–743.Google Scholar

[166] A. A., Lushnikov, M., Kulmala. Singular self-preserving regimes of coagulation processes. Phys. Rev. E 65 (2002).Google Scholar

[167] Z.-M., Ma, M., Röckner. Introduction to the Theory of Non-Symmetric Dirichlet Forms. Springer, 1992.

[168] P., Mandl. Analytic Treatment of One-Dimensional Markov Processes. Springer, 1968.

[169] A.H., Marcus. Stochastic coalescence. Technometrics 10 (1968), 133–143.Google Scholar

[170] R. H., Martin. Nonlinear Operators and Differential Equations in Banach Spaces. Wiley, 1976.

[171] N., Martin, J., England. Mathematical Theory of Entropy. Addison-Wesley, 1981.

[172] V. P., Maslov. Perturbation Theory and Asymptotical Methods. Moscow State University Press, 1965 (in Russian). French Translation, Dunod, Paris, 1972.

[173] V. P., Maslov. Complex Markov Chains and Functional Feynman Integrals. Moscow, Nauka, 1976 (in Russian).

[174] V. P., Maslov. Nonlinear averaging axioms in financial mathematics and stock price dynamics. Theory Prob. Appl. 48:04 (2004), 723–733.Google Scholar

[175] V. P., Maslov. Quantum Economics. Moscow, Nauka, 2006 (in Russian).

[176] V.P., Maslov, G. A., Omel'yanov. Geometric Asymptotics for Nonlinear PDE. I. Translations of Mathematical Monographs, vol. 202, American Mathematical Society, 2001.

[177] V. P., Maslov, C. E., Tariverdiev. Asymptotics of the Kolmogorov-Feller equation for systems with a large number of particles. Itogi Nauki i Techniki. Teoriya veroyatnosti, vol. 19, VINITI, Moscow, 1982, pp. 85-125 (in Russian).

[178] N. B., Maslova. Existence and uniqueness theorems for the Boltzmann equation. In: Ya., Sinai (ed.), Encyclopaedia of Mathematical Sciences, vol. 2, Springer, 1989, pp. 254-278.

[179] N.B., Maslova. Nonlinear Evolution Equations: Kinetic Approach. World Scientific, 1993.

[180] W. M., McEneaney. A new fundamental solution for differential Riccati equations arising in control. Automatica (J. IFAC) 44:4 (2008), 920–936.Google Scholar

[181] H. P., McKean. A class of Markov processes associated with nonlinear parabolic equations. Proc. Nat. Acad. Sci. 56 (1966), 1907–1911.Google Scholar

[182] H. P., McKean. An exponential formula for solving Boltzmann's equation for a Maxwellian gas. J. Combin. Theory 2:3 (1967), 358–382.Google Scholar

[183] M. M., Meerschaert, H.-P., Scheffler. Limit Distributions for Sums of Independent Random Vectors. Wiley Series in Probability and Statistics, John Wiley and Son, 2001.

[184] M. M., Meerschaert, H.-P., Scheffler. Limit theorems for continuous-time random walks with infinite mean waiting times. J. Appl. Prob. 41 (2004), 623–638.Google Scholar

[185] S., Méléard. Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations. Stocha. Stoch. Rep. 63: 3-4 (1998), 195–225.Google Scholar

[186] R., Metzler, J., Klafter. The random walk's guide to anomalous diffusion: a fractional dynamic approach. Phys. Rep. 339 (2000), 1–77.Google Scholar

[187] P.-A., Meyer. Quantum Probability for Probabilists. Springer Lecture Notes in Mathematics, vol. 1538, Springer, 1993.

[188] S., Mishler, B., Wennberg. On the spatially homogeneous Boltzmann equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 16:4 (1999), 467–501.Google Scholar

[189] M., Mobilia, I.T., Georgiev, U.C., Tauber. Phase transitions and spatio-temporal fluctuations in stochastic lattice Lotka-Volterra models. J. Stat. Phys. 128: 1-2 (2007), 447–483.Google Scholar

[190] E.W., Montroll, G. H., Weiss. Random walks on lattices, II. J. Math. Phys. 6 (1965), 167–181.Google Scholar

[191] C., Mouhot, C., Villani. Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Arch. Ration. Mech. Anal. 173:2 (2004), 169–212.Google Scholar

[192] A., Negoro. Stable-like processes: construction of the transition density and the behavior of sample paths near t = 0. Osaka J. Math. 31 (1994), 189–214.Google Scholar

[193] J., Norris. Markov Chains. Cambridge University Press, 1998.

[194] J., Norris. Cluster coagulation. Commun. Math. Phys. 209 (2000), 407–435.Google Scholar

[195] J., Norris. Notes on Brownian coagulation. Markov Proc. Relat. Fields 12:2 (2006), 407–412.Google Scholar

[196] D., Nualart. The Malliavin Calculus and Related Topics. Probability and its Applications, second edition. Springer, 2006.

[197] R., Olkiewicz, L., Xu, B., Zegarlin'ski. Nonlinear problems in infinite interacting particle systems. Inf. Dim. Anal. Quantum Prob. Relat. Topics 11:2 (2008), 179–211.Google Scholar

[198] S., Peszat, J., Zabczyk. Stochastic Partial Differential Equations with Lévy Noise. Encyclopedia of Mathematics, Cambridge University Press, 2007.

[199] D. Ya., Petrina, A. K., Vidibida. Cauchy problem for Bogolyubov's kinetic equations. TrudiMat. Inst. USSR Acad. Sci. 136 (1975), 370–378.Google Scholar

[200] N. I., Portenko, S. I., Podolynny. On multidimensional stable processes with locally unbounded drift. Random Oper. Stoch. Eq. 3:2 (1995), 113–124.Google Scholar

[201] L., Rass, J., Radcliffe. Spatial Deterministic Epidemics. Mathematical Surveys and Monographs, vol. 102, American Mathematical Society, 2003.

[202] S., Rachev, L., Rüschendorf. Mass Transportation Problems, vols. I, II. Springer, 1998.

[203] R., Rebolledo. La methode des martingales appliquée l'etude de la convergence en loi de processus (in French). Bull. Soc. Math. France Mem. 62, 1979.Google Scholar

[204] R., Rebolledo. Sur l'existence de solutions certains problemes de semimartin-gales (in French). C. R. Acad. Sci. Paris A-B 290:18 (1980), A843-A846.Google Scholar

[205] M., Reed, B., Simon. Methods of Modern Mathematical Physics, vol. 1, Functional Analysis. Academic Press, 1972.

[206] M., Reed, B., Simon. Methods of Modern Mathematical Physics, vol. 2, Harmonic Analysis. Academic Press, 1975.

[207] M., Reed, B., Simon. Methods of Modern Mathematical Physics, vol. 4, Analysis of Operators. Academic Press, 1978.

[208] T., Reichenbach, M., Mobilia, E., Frey. Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model. Phys. Rev. E(3) 74:5 (2006).Google Scholar

[209] D., Revuz, M., Yor. Continuous Martingales and Brownian Motion. Springer, 1999.

[210] Yu. A., Rozanov. Probability Theory, Stochastic Processes and Mathematical Statistics (in Russian). Moscow, Nauka, 1985. English translation: Mathematics and its Applications, vol. 344, Kluwer, 1995.

[211] R., Rudnicki, R., Wieczorek. Fragmentation-coagulation models of phytoplankton. Bull. Polish Acad. Sci. Math. 54:2 (2006), 175–191.Google Scholar

[212] V. S., Safronov. Evolution of the Pre-Planetary Cloud and the Formation of the Earth and Planets. Moscow, Nauka, 1969 (in Russian). English translation: Israel Program for Scientific Translations, Jerusalem, 1972.

[213] A. I., Saichev, W. A., Woyczynski. Distributions in the Physical and Engineering Sciences vol. 1, Birkhäuser, Boston, 1997.

[214] A.I., Saichev, G.M., Zaslavsky. Fractional kinetic equations: solutions and applications. Chaos 7:4 (1997), 753–764.Google Scholar

[215] S. G., Samko. Hypersingular Integrals and Applications. Rostov-na-Donu University Press, 1984 (in Russian).

[216] S. G., Samko, A. A., Kilbas, O. A., Marichev. Fractional Integrals and Derivatives and Their Applications. Naukla i Teknika, Minsk, 1987 (in Russian). English translation Harwood Academic.

[217] G., Samorodnitski, M. S., Taqqu. Stable Non-Gaussian Random Processes, Stochastic Models with Infinite Variance. Chapman and Hall, 1994.

[218] R. L., Schilling. On Feller processes with sample paths in Besov spaces. Math. Ann. 309 (1997), 663–675.Google Scholar

[219] R., Schneider. Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, 1993.

[220] A. N., Shiryayev. Probability. Springer, 1984.

[221] Ja. G., Sinai, Ju. M., Suchov. On an existence theorem for the solutions of Bogoljubov's chain of equations (in Russian). Teoret. Mat. Fiz. 19 (1974), 344–363.Google Scholar

[222] F., Sipriani, G., Grillo. Nonlinear Markov semigroups, nonlinear Dirichlet forms and applications to minimal surfaces. J. Reine Angew. Math. 562 (2003), 201–235.Google Scholar

[223] A. V., Skorohod. Stochastic Equations for Complex Systems. Translated from the Russian. Mathematics and its Applications (Soviet Series), vol. 13, Reidel, 1988.

[224] J., Smoller. Shock Waves and Reaction-Diffusion Equations. Springer, 1983.

[225] H., Spohn. Large Scaling Dynamics of Interacting Particles. Springer, 1991.

[226] D. W., Stroock. Diffusion processes associated with Lévy generators. Z. Wahrsch. verw. Gebiete 32 (1975), 209–244.Google Scholar

[227] D. W., Stroock. Markov Processes from K. Ito's Perspective. Annals of Mathematics Studies. Princeton University Press, 2003.

[228] D., Stroock, S. R. S., Varadhan. On degenerate elliptic-parabolic operators of second order and their associated diffusions. Commun. Pure Appl. Math. XXV (1972), 651–713.Google Scholar

[229] D. W., Stroock. S. R. S., Varadhan. Multidimensional Diffusion Processes. Springer, 1979.

[230] A.-S., Sznitman. Nonlinear reflecting diffusion process and the propagation of chaos and fluctuation associated. J. Funct. Anal. 56 (1984), 311–336.Google Scholar

[231] A.-S., Sznitman. Equations de type de Boltzmann, spatialement homogènes. Z. Wahrsch. verw. Gebeite 66 (1984), 559–592.Google Scholar

[232] A.-S., Sznitman. Topics in propagation of chaos. In: Proc. Ecole d'Eté de probabilités de Saint-Flour XIX-1989. Springer Lecture Notes in Mathematics, vol. 1464, Springer, 1991, pp. 167-255.

[233] K., Taira. On the existence of Feller semigroups with boundary conditions. Mem. Ameri. Math. Soc. 99 (1992), 1–65.Google Scholar

[234] K., Taira. On the existence of Feller semigroups with Dirichlet conditions. Tsukuba J. Math. 17 (1993), 377–427.Google Scholar

[235] K., Taira. Boundary value problems for elliptic pseudo-differential operators II. Proc. Roy. Soc. Edinburgh 127A (1997), 395–105.Google Scholar

[236] K., Taira, A., Favini and S., Romanelli. Feller semigroups and degenerate elliptic operators with Wentzell boundary conditions. Stud. Math. 145: 1 (2001), 17–53.Google Scholar

[237] D., Talay, L., Tubaro (eds.). Probabilistic Models for Nonlinear Partial Differential Equations. In: Proc. Conf. at Montecatini Terme, 1995, Springer Lecture Notes in Mathematics, vol. 1627, Springer, 1996.

[238] H., Tanaka. Purely discontinuous Markov processes with nonlinear generators and their propagation of chaos (in Russian). Teor. Verojatnost. i Primenen 15 (1970), 599–621.Google Scholar

[239] H., Tanaka. On Markov process corresponding to Boltzmann's equation of Maxwellian gas. In: Proc. Second Japan-USSR Symp on Probability Theory, Kyoto, 1972, Springer Lecture Notes in Mathematics, vol. 330, Springer, 1973, pp. 478-489.

[240] H., Tanaka, M., Hitsuda. Central limit theorems for a simple diffusion model of interacting particles. Hiroshima Math. J. 11 (1981), 415–423.Google Scholar

[241] V. V., Uchaikin, V.M., Zolotarev. Chance and Stability: Stable Distributions and their Applications. VSP, 1999.

[242] V. V., Uchaikin. Montroll-Weisse problem, fractional equations and stable distributions. Int. J. Theor. Phys. 39:8 (2000), 2087–2105.Google Scholar

[243] K., Uchiyama. Scaling limit of interacting diffusions with arbitrary initial distributions. Prob. Theory Relat. Fields 99 (1994), 97–110.Google Scholar

[244] J.M., van Neerven. Continuity and representation of Gaussian Mehler semigroups. Potential Anal. 13:3 (2000), 199–211.Google Scholar

[245] C., Villani. On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Ration. Mech. Anal. 143 (1998), 273–307.Google Scholar

[246] C., Villani. Topics in Optimal Transportation. Graduate Studies in Mathematics vol. 58, American Mathematical Society, 2003.

[247] W., Whitt. Stochastic-Process Limits. Springer, 2002.

[248] E. T., Whittaker, G. N., Watson. Modern Analysis, third edition. Cambridge University Press, 1920.

[249] D., Wrzosek. Mass-conservation solutions to the discrete coagulation-fragmentation model with diffusion. Nonlinear Anal. 49 (2002), 297–314.Google Scholar

[250] K., Yosida. Functional Analysis. Springer, 1980.

[251] M., Zak. Dynamics of intelligent systems. Int. J. Theor. Phys. 39:8 (2000), 2107–2140.Google Scholar

[252] M., Zak. Quantum evolution as a nonlinear Markov process. Found. Phys. Lett. 15:3 (2002), 229–243.Google Scholar

[253] G. M., Zaslavsky. Fractional kinetic equation for Hamiltonian chaos. Physica D 76 (1994), 110–122.Google Scholar

[254] B., Zegarlinski. Linear and nonlinear phenomena in large interacting systems. Rep. Math. Phys. 59:3 (2007), 409–419.Google Scholar

[255] V. M., Zolotarev. One-Dimensional Stable Distributions. Moscow, Nauka, 1983 (in Russian). English translation: Translations of Mathematical Monographs, vol. 65, American Mathematical Society, 1986.