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.