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Published online by Cambridge University Press:  07 November 2024

Daniel W. Stroock
Daniel W. Stroock
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Massachusetts Institute of Technology
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Probability Theory, An Analytic View , pp. 437 - 439
Publisher: Cambridge University Press
Print publication year: 2024

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References

Beckner, W. (1975). Inequalities in Fourier analysis. Ann. Math. 102(1), 159–182.CrossRefGoogle Scholar
Billingsley, P. (1968). Convergence of Probability Measures. Wiley.Google Scholar
Bingham, N., Goldie, C., & Teugels, J. (1987). Regular Variation. Cambridge University Press.CrossRefGoogle Scholar
Bobkov, S. G. (1997). An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space. Ann. Probab. 25(1), 206–214.CrossRefGoogle Scholar
Borell, C. (1975). The Brunn–Minkowski inequality in Gauss space. Invent. Math. 30(2), 207–216.CrossRefGoogle Scholar
Brelot, M. (1965). Éléments de la Théorie Classique du Potentiel. Centre de Documentation Universitaire, Sorbonne, Paris V.Google Scholar
Choquet, G. (1965). Lectures on Analysis, Vol. I. W. A. Benjamin.Google Scholar
Chung, K.-L. (1973). Probabilistic approach in potential theory to the equilibrium problem. Ann. Inst. Fourier Gren. 23(3), 313–322.Google Scholar
Bolthausen, E. (1984). An estimate of the remainder term in a combinatorial central limit theorem. Z. Wahr. Gebiete 66, 379–386.Google Scholar
Borel, E. (1906). Sur les principes de la cinétique des gaz. Ann. l’École Norm. Sup., Ser. 3 23, 9–32.Google Scholar
Burkholder, D. (1991). Explorations in Martingale Theory and Its Applications. 1989 Saint-Flour Ecole d’Eté Lectures, Springer LNM 1464.CrossRefGoogle Scholar
Carne, T. H. (1985). A transmutation formula for Markov chains. Bull. Sc. Math. 109, 399–405.Google Scholar
Courant, R., Friedrichs, K., & Lewy, H. (1928). Über die partiellen differenzengleichungen der mathematischen physik. Math. Ann. 100, 32–74.CrossRefGoogle Scholar
Deuschel, J.-D. & Stroock, D. (1988). Large Deviations. AMS Chelsea Publishing.Google Scholar
Doob, J. L. (1953). Stochastic Processes. Wiley.Google Scholar
Doob, J. L. (1954). Semimartingales and subharmonic functions. Trans. Am. Math. Soc. 77, 86–121.CrossRefGoogle Scholar
Doob, J. L. (1984). Classical Potential Theory and Its Probabilistic Counterpart. Springer.CrossRefGoogle Scholar
Dudley, R. M. (2002). Real Analysis and Probability. Cambridge Studies in Advanced Mathematics. Cambridge University Press.Google Scholar
Durrett, R. (2019). Probability: Theory and Examples, 5th ed. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press.CrossRefGoogle Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vols. I & II. Wiley.Google Scholar
Feller, W. (1968). An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech. 18(4), 345–355.Google Scholar
Gordon, C., Webb, D., & Wolpert, S. (1992). One cannot hear the shape of a drum. Bull. Am. Math. Soc., New Series, 27, 134–138.Google Scholar
Gross, L. (1967). Abstract Wiener spaces. Pages 31–42 in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2. University of California Press.Google Scholar
Gross, L. (1975). Logarithmic Sobolev inequalities. Am. J. Math. 97(4), 1061–1083.CrossRefGoogle Scholar
Hartman, P. (1947). On the ergodic theorem. Am. J. Math. 69, 193–199.CrossRefGoogle Scholar
Hunt, G. (1956). Some theorems concerning Brownian motion. Trans. Am. Math. Soc. 81, 294–319.CrossRefGoogle Scholar
Hunt, G. (1957–1958). Markov processes and potentials I, II, & III. Ill. J. Math. 1, 44–3; 1, 313–369; 2, 151–213.Google Scholar
Itô, K. (1951). On stochastic differential equations. Memoirs Am. Math. Soc. 4.CrossRefGoogle Scholar
Kac, M. (1951). On some connections between probability theory and differential and integral equations. Pages 189–214 in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press.Google Scholar
Kac, M. (1966). Can one hear the shape of a drum? Am. Math. Monthly 73(4P2), 1–23.Google Scholar
Kakutani, S. (1944). Two-dimensional Brownian motion and harmonic functions. Proc. Imp. Acad. Tokyo 20(10), 706–714.Google Scholar
Kakutani, S. (1949). Markoff process and the Dirichlet problem. Proc. Imp. Acad. Tokyo 21(4), 227–233.Google Scholar
Kellog, O. D. (1963). Foundations of Potential Theory. Dover.Google Scholar
Krylov, N. (1996). Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Math. 12. American Mathematical Society.Google Scholar
Kunita, H. & Watanabe, S. (1967). On square integrable martingales. Nagoya Math. J. 30, 209–245.CrossRefGoogle Scholar
Kuo, H. (1975). Gaussian Measures in Banach Spaces. Springer LNM 463.Google Scholar
Kuratowski, C. (1933). Topologie, Vol. I. Instytut Matematyczny Polskiej Akademii Nauk.Google Scholar
Lorentz, G. (1986). Bernstein Polynomials. Chelsea Publishing Co.Google Scholar
Ledoux, M. & Telegrand, M. (1991). Probability in Banach Spaces. Ergebnisse, Series 3, Springer.CrossRefGoogle Scholar
Lieb, E. (1990). Gaussian kernels have only Gaussian maximizers. Invent. Math. 12, 179–208.Google Scholar
Loève, M. (1955). Probability Theory. D Van Nostrand.Google Scholar
Mehler, F. G. (1866). Über die entwicklungen einer funktion von beliebig vielen variabeln nach Laplaceshen funktionen höherer ordnung. J. Reine und Angewandte Math. 66, 161–176.Google Scholar
Mourier, E. (1953). Eléments aléatoires dans un espace de Banach. Ann. Inst. Poincaré 13, 166–244.Google Scholar
Nelson, E. (1974). The free Markov field. J. Funct. Anal. 12, 12–21.Google Scholar
Neveu, J. (1975). Discrete-Parameter Martingales. North–Holland.Google Scholar
Phillips, H. & Wiener, N. (1923). Nets and Dirichlet problem. J. Math. and Phys. 2, 105–124.CrossRefGoogle Scholar
Port, S. & Stone, C. (1978). Brownian Motion and Classical Potential Theory. Academic Press.Google Scholar
Prohorov, Yu. V. (1956). Convergence of random processes and limit theorems in probability theory. Theory Prob. Appl. 1(2), 177–238.Google Scholar
Ranga, R. (1963). The law of large numbers for D [0, 1]-valued random variables. Theory Prob. Appl. 8(1), 75–79.Google Scholar
Revuz, D. & Yor, M. (1999). Continuous Martingales and Brownian Motion. Grundlehren Series in Mathematics. Springer.Google Scholar
Segal, I. (1957). Ergodic subgroups of the orthogonal group on a real Hilbert space. Ann. Math. 66(2), 297–303.CrossRefGoogle Scholar
Segal, I. (1958). Distributions in Hilbert space and canonical systems of operators. Trans. Am. Math. Soc., 88, 12–41.CrossRefGoogle Scholar
Sharpe, M. (1988). General Theory of Markov Processes. Academic Press.Google Scholar
Skorohod, A. V. (1982). Studies in the Theory of Random Processes. Dover.Google Scholar
Spitzer, F. (1964). Electrostatic capacity, heat flow, and Brownian motion. Z. Wahrsh. Ver. Geb. 3, 110–121.Google Scholar
Stein, C. (1986). Approximate Computation of Expectations. Institute of Mathematical Statistics Lecture Notes & Monograph Series 7.CrossRefGoogle Scholar
Stroock, D. (1979). Some remarks about Beckner’s inequality. Pages 149–157 in Proceedings of Symposia in Pure Mathematics, XXXV Part 1. American Mathematical Society.Google Scholar
Stroock, D. (2003). Markov Processes from K. Itô’s Perspective. Annals of Mathematics Studies 155. Princeton University Press.Google Scholar
Stroock, D. (2005). An Introduction to Markov Processes. Graduate Texts in Mathematics. Springer.Google Scholar
Stroock, D. (2010). Some thoughts about Segal’s ergodic theorem. Colloq. Math. 118(1), 89–105.CrossRefGoogle Scholar
Stroock, D. (2020). Essentials of Integration Theory for Analysis, 2nd ed. Graduate Texts in Mathematics. Springer.Google Scholar
Stroock, D. (2023). Gaussian Measures in Finite and Infinite Dimensions. Springer Univeritext.CrossRefGoogle Scholar
Sudakov, V. N. & Tsirel'son, B. S. (1974). Extremal properties of half-spaces for spherically invariant measures. J. Sov. Math. 9(1), 9–18.Google Scholar
Varadarajan, V. S. (1958). Weak convergence of measures on a separable metric spaces. Sankhya¯ 19, 15–22.Google Scholar
Wiener, N. (1923). Differential space. J. Math. Phys. 2, 131–174.CrossRefGoogle Scholar
Wiener, N. (1924). Certain notions in potential theory. J. Math. Phys. 3, 24–51.CrossRefGoogle Scholar
Yosida, K. (1988). Functional Analysis. Classics in Mathematics. Springer.Google Scholar

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  • References
  • Daniel W. Stroock, Massachusetts Institute of Technology
  • Book: Probability Theory, An Analytic View
  • Online publication: 07 November 2024
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  • References
  • Daniel W. Stroock, Massachusetts Institute of Technology
  • Book: Probability Theory, An Analytic View
  • Online publication: 07 November 2024
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  • References
  • Daniel W. Stroock, Massachusetts Institute of Technology
  • Book: Probability Theory, An Analytic View
  • Online publication: 07 November 2024
Available formats
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