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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 16, Fasc. 2,
pages 299 - 309
 

ON THE CENTRAL LIMIT THEOREM FOR INDEPENDENT RANDOM VARIABLES WITH ALMOST SURE CONVERGENCE

Beata Rodzik
Zdzisław Rychlik

Abstract: We obtain an almost sure convergence limit theorem for independent nonidentically distributed random variables. Let S , n n > 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 in logarithmic means a(S /(ES2 )1/2) n n converges almost surely to integral oo a(x)dP(x). - oo

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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