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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 26, Fasc. 1,
pages 63 - 76
 

CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR ARRAYS

Victor Kruglov
Andrei Volodin

Abstract: In this paper we present new sufficient conditions for complete convergence for sums of arrays of rowwise independent random variables. These conditions appear to be necessary and sufficient in the case of partial sums of independent identically distributed random variables. Many known results on complete convergence can be obtained as corollaries to theorems proved in this paper.

2000 AMS Mathematics Subject Classification: 60F15, 60GS0.

Key words and phrases: Arrays of rowwise independent random variables, complete convergence, rate of convergence in the law of large numbers.

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