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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 23, Fasc. 2,
pages 241 - 249
 

SOME REMARKS ON THE ALMOST SURE CENTRAL LIMIT THEOREM FOR INDEPENDENT RANDOM VARIABLES

Zdzisław Rychlik
Konrad S. Szuster

Abstract: The purpose of this paper is the proof of an almost sure central limit theorem for subsequences. We obtain an almost sure convergence limit theorem for independent nonidentically distributed random variables. The presented results extend, to nonidentically distributed random variables, theorems given by Schatte [13].

2000 AMS Mathematics Subject Classification: Primary 60F05, 60F15; Secondary 60G50.

Key words and phrases: Functional central limit theorem; almost sure version of the functional central limit theorem; Wiener measure.

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