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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 1, Fasc. 2,
pages 117 - 131
 

ON MARCINKIEWICZ-ZYGMUND LAWS OF LARGE NUMBERS IN BANACH SPACES AND RELATED RATES OF CONVERGENCE

Wojbor A. Woyczyński

Abstract: The paper studies asymptotic almost sure and tail behavior of sums (X + ...+ X )/n1/p, 1 < p < 2, 1 n for independent, centered random vectors X , n = 1,2,..., n taking values in Banach space E . The obtained results are in the spirit of Mazurkiewicz-Zygmund, Hsu-Robbins-Erdös-Spitzer, and Brunk theorems for real random variables and show the essential role played by the geometry of E in the infinite-dimensional case.

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

Key words and phrases: -

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