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Tytuł artykułu

Generalized translation operators and Markov processes

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Języki publikacji
EN
Abstrakty
EN
We study the relationship between generalized translation operators and stochastic convolutions on locally compact spaces. We prove that stochastic convolution semigroups can generate Levy type processes which are strong Markov Feller processes and, as an example, we study the Bingham convolution and its dual on integers.
Wydawca
Rocznik
Strony
295--304
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • Institute of mathematics National Center for Natural Sciences and Technology P.O. Box 631, Boho Hanoi, Vietnam
Bibliografia
  • [1] N. H. Bingham, Random walks on spheres, Z. Wahrscheinlichkeitstheorie Verw. Geb., 22 (1972), 169-192.
  • [2] P. M. Blumenthal and R. K. Getoor, Markov Process and Potential Theory, Academic Press, New York, (1968).
  • [3] S. Bochner, Sturm-Liouville and heat equations whose eigenfunctions are ultraspherical polynomials and associated Bess el functions, Proc. Conference on Differential Equations Maryland, 1955.
  • [4] D. M. Bressound, Linearization and related formulas for q-ultraspherical polynomials, SIAM J. Math. Anal. 12 (1981), 161-168.
  • [5] K. L. Chung, Lectures from Markov Process to Brownian Motion, Springer, New York, 1982.
  • [6] E. B. Dynkin, Markov Processes, I, Springer 1965.
  • [7] H. Heyer, Probability theory on hypergroups: A servey, In H. Heyer (Ed.) Probability measures on groups VII, Lecture Notes in Mathematics, Vol. 1064, Springer, Berlin, pp. 481-550, 1984.
  • [8] R. Lasser, On the Levy-Hincin formula for a commutative hypergroups, in: H. Heyer (Ed.), Probability measures on groups VII. Lecture Notes in Mathematics, Vol. 1064, Springer, Berlin, pp. 298-308, 1984.
  • [9] R. Lasser, Bochner Theorems for hypergroups and their applications to orthogonal polynomial expansions, J. Approx. Theor. 37 (1983), 311-325.
  • [10] B. M. Levitan, Generalized translation operators and some of their applications, Israel Program for Scientific Translations, Jerusalem 1962.
  • [11] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999.
  • [12] T. Shiga and S. Wantanabe, Bessel diffusions as a one-parameter family of diffusion processes, Z. Wahrscheinlichkeitstheorie Verw. Geb. 27 (1973), 34-46.
  • [13] N. V. Thu, Generalized independent increments processes, Nagoya Math. J. 133 (1994), 155-175.
  • [14] K. Urbanik, Generalized convolutions, Studia Math. 23 (1964), 217-245.
  • [15] V. E. Vol'kovich, On an analytical description of Urbanik algebras, Izv. Akad. Nauk. UzSSR Ser. Fiz. Math. Nauk, 5 (1979), 12-17.
  • [16] V. E. Vol'kovich, On symmetric stochastic convolutions, J. Theor. Prob. 5, No 3 (1992), 117-430.
  • [17] G. N. Watson, A Treatise on Bessel Functions, Sec. Ed. Cambridge University Press, 1966.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0038-0016
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