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Contents of PMS, Vol. 23, Fasc. 2,
pages 305 - 313
 

ON EXACT STRONG LAWS FOR SUMS OF MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES

André Adler
Yongcheng Qi

Abstract: Let (X,X ,n (- Zd ) n + be independent and identically distributed random variables satisfying xP (| X |> x) ~~ L(x) with either EX = 0 or E|X |= oo , where L(x) is slowly varying at infinity. This paper proves that there always exist sequences of constants (a ) n and (B ) N such that an Exact Strong Law holds, that is

sum a X /B --> 1 almostsurely asN --> oo . n n N |n|<N

2000 AMS Mathematics Subject Classification: Primary 60F15.

Key words and phrases: Strong law of large numbers, almost sure convergence, exact strong laws, multidimensionally indexed random variables.

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