This article is cited in 10 papers

Limit theorems for the maximal random sums

V. M. Kruglov, Zhang Bo

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Necessary and sufficient conditions are given for monotone sequences of scaled random variables with a random index to converge weakly or converge weakly with the mixing property in Rényi's sense. The main results are related with the case when the terms of the sequences are sequential maximal sums of independent random variables.

Keywords: weak convergence, mixing property in Rényi's sense, maximalsum of random variables, random variable.

Received: 06.02.1995

DOI: 10.4213/tvp3132

 English version: Theory of Probability and its Applications, 1997, 41:3, 468–478

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