On strong versions of the central limit theorem

Zdzislaw Rychlik and Konrad S. Szuster

Statistics & Probability Letters, 2003, vol. 61, issue 4, 347-357

Abstract: The purpose of this paper is to present strong versions of the central limit theorem for independent nonidentically distributed random variables. Let Sn, n[greater-or-equal, slanted]1, be the partial sums of independent random variables with zero means and finite variances and let a(x) be a real function. We present sufficient conditions under which the arithmetic means of a(Snk/(ESnk2)1/2) converge almost surely to for some subsequences {nk, k[greater-or-equal, slanted]1}, where [Phi] denotes the standard normal distribution.

Keywords: Central; limit; theorem; Pointwise; central; limit; theorem; Summation; methods (search for similar items in EconPapers)
Date: 2003
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