This is a preview of subscription content, log in via an institution to check access.
Literature cited
W. Stout, “Almost sure invariance principles when Ex 21 =∞,” Z. Wahrsch. Verw. Geb.,49, No. 1, 23–32 (1979).
N. M. Zinchenko, “Strong invariance principle for sums of random variables from the domain of attraction of a stable law,” Reor. Veroyatn. Primen.,30, No. 1, 131–136 (1985).
E. Fisher, “An almost sure invariance principle for random variables in the domain of attraction of a stable law,” Z. Wahrsch. Verw. Geb.,67, No. 4 (1984).
J. Mijnheer, “Strong approximation of partial sums of the i.i.d.r.v. in the domain of attraction of a symmetric stable distribution,” in: Trans, of the Ninth Prague Conference on Inf. Theory, Statist. Decision Functions, Random Processes, Prague (1983), pp. 85–89.
M. Csörgo and P. Revesz, Strong Approximation in Probability and Statistics, Akademia, Budapest (1981).
V. N. Paulauskas, “Estimates of the error term in the limit theorem in the case of a stable limit law,” Lit. Mat. Sb.,14, No. 1, 165–187 (1974).
N. B. Kalinauskaite, “Upper and lower functions for stable processes,” Liet. Mat. Rinkiys,5, No. 4, 541–553 (1965).
N. M. Zinchenko, “Rate of growth of stochastic processes and fields with independent increments,” Teor. Veroyatn. Mat. Statistika, No. 30, 52–56 (1984).
M. D. Donsker and S. R. S. Varadhan, “On LIL for local times,” Commun. Pure Appl. Math.,30, No. 6, 707–753 (1977).
N. C. Jain, “A Donsker-Varadhan type invariance principle,” Z. Wahrsch. Verw. Geb.,59, No. 2, 117–138 (1982).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 6, pp. 713–718, November–December, 1986.
Rights and permissions
About this article
Cite this article
Zinchenko, N.M. Asymptotics of sums of random variables from the domain of attraction of a stable law. Ukr Math J 38, 598–603 (1986). https://doi.org/10.1007/BF01056642
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01056642