ON EXACT STRONG LAWS OF LARGE NUMBERS UNDER GENERAL
DEPENDENCE CONDITIONS

André Adler

Przemysław Matuła

Abstract: We study the almost sure convergence of weighted sums of dependent random
variables to a positive and finite constant, in the case when the random variables have either
mean zero or no mean at all. These are not typical strong laws and they are called exact strong
laws of large numbers. We do not assume any particular type of dependence and furthermore
consider sequences which are not necessarily identically distributed. The obtained
results may be applied to sequences of negatively associated random variables.

2010 AMS Mathematics Subject Classification: Primary: 60F15; Secondary:
60F05.

Keywords and phrases: Strong law of large numbers, almost sure convergence, slowly
varying functions, negative association.