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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 1,
pages 99 - 111
 

RATE OF CONVERGENCE IN THE STRONG LAW OF LARGE NUMBERS

Sándor Csörgő
Zdzisław Rychlik

Abstract: Let (Xn,n > 1) be a sequence of independent random variables such that EXn = 0,EX2n = s2n < oo , n > 1. For each n > 1 let

n n S = sum X , S2 = sum s2; n k=1 k n k=1 k
then, under some additional conditions, 1+a Sn/S n --> 0 as n --> oo with probability 1 for any a > 0.

The main purpose of this paper is to give the order of magnitude of

oo sum P(|Sn|> tS1n+2a) n=1
as + t-- > 0 . The rate of convergence in the random strong law of large numbers is established too.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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