On the law of large numbers for stationary sequences

R. A. Maller

Stochastic Processes and their Applications, 1980, vol. 10, issue 1, 65-73

Abstract: We show that if Xi is a stationary sequence for which Sn/Bn converges to a finite non zero random variable of constant sign, where Sn=X1+X2+...+Xn and Bn is a sequence of constants, then Bn is regularly varying with index 1. If in addition [Sigma]P(X1>Bn is finite, then EX1 is finite, and if in addition to this Xi satisfies an asymptotic independence condition, EX1 [not equal to] 0.

Date: 1980
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