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Generalized independent increments processes(*)

Published online by Cambridge University Press:  22 January 2016

Nguyen Van Thu*
Affiliation:
Institute of Mathematics, Hanoi, P.O. Box 631 Boho, 10000 Hanoi, Vietnam
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We study a class of Markov processes which arise in the theory of generalized convolutions and stand for a generalization of processes with independent increments.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

Footnotes

Dedicated to Professor K. Urbanik on his 60th birthday

The paper was supported in part by the National Basic Research Program in Natural Science, Vietnam.

(*)

The research was carried out during the author’s stay at Technische Universität Berlin (1988) and at Nagoya Institute of Technology (1989) under grants from Alexander von Humboldt-Stiftung and the Japan Society for the Promotion of Science.

References

[1] Berg, C., and Forst, G. Potential theory on locally compact Abelian groups, Springer-Verlag, Berlin Heidelberg New York (1975).CrossRefGoogle Scholar
[2] Bingham, N.H. On a theorem of Klosowska about generalized convolutions, Coll. Math., 48, (1984), 117125.CrossRefGoogle Scholar
[3] Blumenthal, R. M., Getoor, R. K. Markov processes and potential theory, Academic Press, New York, (1968).Google Scholar
[4] Cambanis, S., Keener, R. and Simons, G. On a-symmetric multivariate distributions, J. Multivariate Anal., 13, (1983), 213233.Google Scholar
[5] Chung, K.L. Lectures from Markov processes to Brownian motion, Springer-Verlag, New York Heidelberg Berlin, (1982).CrossRefGoogle Scholar
[6] Dharmadhikari, S.W. and Joagdev, K. Unimodality, convexity and applications, Academic Press, San Diego (1988).Google Scholar
[7] Dynkin, E. B. Markov Processes, I. Springer-Verlag, Berlin (1965).Google Scholar
[8] Gradshteyn, I.S. and Ryzhik, I.M. Tables of integrals, series and products, Academic Press, San Diego (1980).Google Scholar
[9] Hudson, W.N., Mason, J. David, Operator self-similar processes in a finite-dimensional space, Trans. Amer. Math. Soc, 273 (1) (1982), 281297.CrossRefGoogle Scholar
[10] Kingman, J.F.C. Random walks with spherical symmetry, Acta Math., 109 (1963), 1153.CrossRefGoogle Scholar
[11] Klosowska, M. On the domain of attraction for generalized convolution algebras. Re. Roumaine Math. Pures Appl. 22 (1977), 669677.Google Scholar
[12] Kucharczak, J., Decomposability of point measures in generalized convolution algebras, Colloq. Math., 55 (1988). 163167.Google Scholar
[13] Lamperti, J., Semistable stochastic processes, Trans. Amer. Math. Soc, 104 (1962), 6278.CrossRefGoogle Scholar
[14] Levitan, B.M., Generalized translation operators and some of their applications, Israel Program for Scientific Translations, Jerusalem 1962.Google Scholar
[15] Sato, K., Distributions of class L and self-similar processes with independent increments, in “White Noise Analysis” edited by Hida, T. et al., World Scientific, Singapore, (1990) pp. 360373.Google Scholar
[16] Urbanik, K. Generalized convolutions, Studia Math., 23 (1964), 217245.CrossRefGoogle Scholar
[17] Urbanik, K., Generalized convolutions II, Studia Math., 45 (1973), 5770.Google Scholar
[18] Urbanik, K., Generalized convolutions III, Studia Math., 80 (1984), 167189.CrossRefGoogle Scholar
[19] Urbanik, K., Generalized convolutions IV, Studia Math., 83 (1986), 5795.CrossRefGoogle Scholar
[20] Urbanik, K., Domain of attraction and moments, Probab. Math. Statist, 8 (1987), 89101.Google Scholar
[21] Urbanik, K., Quasi-regular generalized convolutions, Colloq. Math., 55 (1988), 147162.CrossRefGoogle Scholar
[22] Urbanik, K., Generalized convolutions V, Studia Math., 91 (1988), 153178.Google Scholar
[23] Vol’kovich, V.E., On an analytical description of Urbanik algebras, Izv. Akad. Nauk. UzSSR Ser. Fiz-Math. Nauk, 5 (1979), 1217.Google Scholar
[24] Wintner, A., Asymptotic distributions and infinite convolutions, Edwards Brothers, Ann Arbor, Michigan (1938).Google Scholar