On the law of large numbers for stationary in the narrow sense sequences

Abstract

In his recent work published in Vestnik SPbSU, Ser. 1, V. V. Petrov found new sufficient conditions for the strong law of large numbers for the stationary in the broad sense sequences of random variables. These conditions are expressed in the terms of the second moments. In my work with the aid of the ergodic theorem analogous problems are solved for the sequences of stationary in the narrow sense random variables. In the absence the second moments for the formulation of conditions are used the second moments of the truncated random variables. At the end of the article is given an example to the stationary sequence of random variables, which is not ergodic, but for which is valid the strong law of large numbers. Refs 3.