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Estimates of the rate of convergence in the strong law of large numbers. (Russian) Zbl 0569.60027

Let \(x_ 1,x_ 2,..\). be a sequence of independent random variables, \(S_ n=x_ 1+...+x_ n\), \(F_ k(x)=P\{x_ k<x\}\), \(k=1,2,... \). The rate of convergence to zero of the probability \(P\{\) \(\sup_{k\geq n}| S_ k/b_ k-A_ k| >\epsilon \}\) with \(n\to \infty\) is studied, where \(\epsilon >0\), \(A_ n=b_ n^{- 1}\sum^{n}_{k=1}\int^{b_ n}_{-b_ n}xdF_ k(x)\) and \(b_ n's\) are constants. Several theorems are proved where the estimators of such convergence rates are given.
Reviewer: I.Bokuchava

MSC:

60F15 Strong limit theorems
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