This is a preview of subscription content, log in via an institution to check access.
Literature cited
R. Gangolli, “Isotropic infinitely divisible measures on symmetric space,” Acta Math.,111, 213–246 (1964).
J. F. Kingman, “Random walks with spherical symmetry,” Acta Math.,109, 11–53 (1963).
S. Bochner, “Positive zonal functions on spheres,” Proc. Nat. Acad. Sci. USA,40, 1141–1147 (1954).
I. J. Schonberg, “Positive-definite functions on spheres,” Duke Math., J.,9, 96–108 (1942).
M. Kennedy, “A stochastic process associated with the ultraspherical polynomials,” Proc. R. Irish Acad., sec. A,61, 89–100 (1961).
K. R. Getoor, “Infinitely divisible probabilities on the hyperbolic plane,” Pac. J. Math.,11, 1287–1308 (1961).
K. Urbanik, “Generalized convolutions,” Stud. Math.,23, 217–245 (1964).
K. Urbanik, Generalized Convolutions IV, Preprint No. 17, Math. Inst. Univ. Wroclaw (1984).
R. Lasser, “On the Levy-Khinchin formula for commutative hypergroups,” Lect. Notes Math.,1064, 298–308 (1983).
H. Heyer, “Probability theory on hypergroups,” Lect. Notes Math., Vol. 1064, 482–550 (1983).
F. I. Karpelevich, V. N. Tutubalin, and M. G. Shur, “Limit theorems for compositions of distributions on a Lobachevskii plane and in Lobachevskii space,” Teor. Veroyatn. Primen.,4, 432–436 (1959).
V. N. Tutubalin, “On limiting behavior of compositions of measures on a Lobachevskii plane and in Lobachevskii space,” Teor. Veroyatn. Primen.,7, 197–204 (1962).
B. M. Levitan, “On one class of solutions of the Kolmogorov-Smoluchowski equation,” Vestn. Leningr. Gos. Univ. Ser. Math.,7, No. 2, 81–115 (1960).
V. E. Vol'kovich, “On infinitely divisible distributions in algebras with stochastic convolution,” in: Stability Problems of Stochastic Models, Proceedings of a Seminar [in Russian], VNIISI, Moscow (1985), pp. 15–24.
I. V. Ostrovskii, “Description of the class I0 in one special semigroup of probability measures,” in: Math. Phys. and Functional Analysis [in Russian], No. 4, FTIT AN UkrSSR (1973), pp. 3–12.
I. V. Ostrovskii and I. P. Trukhina, “On the arithmetic of Schonberg-Kennedy semigroups,” in: Topics of Math. Phys. and Functional Analysis, Proc. of Scientific Seminars [in Russian], Naukova Dumka, Kiev (1976), pp. 11–19.
I. P. Trukhina, “On semigroups of functions representable by series in Jacobi polynomials,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1, 21–24 (1977).
I. P. Trukhina, “On a problem of J. Lamperti,” Teor. Veroyatn. Primen.,23, No. 4, 869–870 (1978).
I. P. Truykhina, “On one problem connected with the arithmetic of probability measures on a sphere,” J. Sov. Math.,17, No. 6 (1981).
I. P. Trukhina, “Arithmetic of spherical symmetric measures in Lobachevskii space,” in: Theory of Functions, Functional Analysis and Their Applications [in Russian], Vol. 34, Kharkov (1980), pp. 136–146.
A. I. Il'inskii, “On the arithmetic of generalized characteristic functions of B. M. Levitan,” in: Continuity and Stability in Problems of Probability Theory and Mathematical Statistics, J. Sov. Math.,16, No. 5 (1981).
J. Lamperti, “The arithmetic of certain semigroups of positive operators,” Proc. Cambridge Phil. Soc.,64, No. 6, 161–66 (1969).
K. R. Partasarathy, R. Ranga Rao, and S. R. S. Varadhan, “Probability distributions on locally compact abelian groups,” Illinois J. Math.,7, 337–369 (1963).
I. Z. Ruzsa and J. S. Gabor, “Decompositions of probability measures on groups,” Lect. Notes Math.,1064, 409–417 (1983).
Additional information
Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, pp. 19–32, 1987.
Rights and permissions
About this article
Cite this article
Vol'kovich, V.E. Quasiregular stochastic convolutions. J Math Sci 47, 2685–2699 (1989). https://doi.org/10.1007/BF01095593
Issue Date:
DOI: https://doi.org/10.1007/BF01095593