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Contents of PMS, Vol. 2, Fasc. 2,
pages 179 - 192
 

LAWS OF LARGE NUMBERS OF ERDÖS-RÉNYI’S TYPE FOR NON-STATIONARY RANDOM FIELDS

August Micha  Zapa³a

Abstract: Let K < Rr r be the r -dimensional cartesian product of the set of positive integers and let (X ,k (- K ) k r be a random field - a collection of independent, not necessarily identically distributed random variables with mean zero. Under appropriate additional assumptions we derive for (X ,k (- K ) k r strong limit theorems of the same type as the Erdös-Rényi law of large numbers. Our results are based on the large deviation theorem of Petrov extended to random fields.

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

Key words and phrases: -

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