Asymptotics in the Baum–Katz formula for random fields

S. V. Dil'man

M. V. Lomonosov Moscow State University

Abstract: In 1996, D. Deng established an analog of the Baum–Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.

UDC: 519.21

Received: 24.11.2004
Revised: 15.11.2005

DOI: 10.4213/mzm2739

 English version: Mathematical Notes, 2006, 79:5, 625–631

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