This is a preview of subscription content, log in via an institution to check access.
Literature cited
R. L. Dobrushin, “A lemma on the limit of a compound random variable,”Usp. Mat. Nauk,10, No. 2(64), 157–159 (1955).
V. M. Kruglov and V. Yu. Korolev,Limit Theorems for Random Sums [in Russian], Moscow University Press (1990).
G. Siegel, “Limit theorems for sequences with random indices,”Wiss. Sitzung. Stochastik Akad. Wiss. DDR Inst. Math., No. 1 (1981).
A. Gut, “Stopped random walks. Limit theorems and applications,” Uppsala University Manuscript (1986).
D. S. Sil'vestrov,Limit Theorems for Complicated Random Functions [in Russian], Vishcha Shkola, Kiev (1974).
V. V. Anisimov,Stochastic Processes with Discrete Component. Limit Theorems [in Russian], Vishcha Shkola, Kiev (1988).
C. C. Heyde, “Some central limit analogues for supercritical Galton-Watson processes,”J. Appl. Prob.,8, No. 1, 52–59 (1971).
W. Freudenberg and D. Szynal, “Limit laws for a random number of record values,”Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. et Phys.,24, No. 3, 193–199 (1976).
V. Yu. Korolev, “Nonuniform estimates of the stability of a normal law under random perturbations of the scale parameter and some of their applications,”Probl. Ustoich. Stokh. Mod. Tr. Sem., 84–92 (1988).
V. Yu. Korolev, “The asymptotic distributions of random sums,”Lect. Notes Math., No. 1307, 97–105 (1989).
V. M. Kruglov,Supplementary Chapters in Probability Theory [in Russian], Vysshaya Shkola, Moscow (1984).
L. V. Kantorovich and G. P. Akilov,Functional Analysis in Normed Spaces, Pergamon Press, New York (1964).
V. Yu. Korolev, “Approximation of the distributions of sums of a random number of independent random variables by mixtures of normal laws,”Teor. Veroyatn. i Prim.,34, No. 3, 581–588 (1989).
V. M. Kruglov, “Convergence of the moments of random sums,”Teor. Veroyatn. i Prim.,33, No. 2, 360–363 (1988).
M. Sharpe, “Operator-stable probability measures on vector groups,”Trans. Amer. Math. Soc.,136, 51–65 (1969).
J. Galambos,The Asymptotic Theory of Extreme Order Statistics, Wiley, New York (1978).
B. V. Gnedenko and D. B. Gnedenko, “On the Laplace and logistic distributions as limits in probability theory,”Serdika,8, No. 2, 229–234 (1982).
B. V. Gnedenko, “On limit theorems for a random number of random variables,”Lect. Notes Math., No. 1021, 167–176 (1983).
Additional information
Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 60–72.
Rights and permissions
About this article
Cite this article
Korolev, V.Y. The asymptotics of randomly indexed random sequences: Independent indices. J Math Sci 59, 926–938 (1992). https://doi.org/10.1007/BF01099121
Issue Date:
DOI: https://doi.org/10.1007/BF01099121