On the strong convergence of weighted sums

Rita Giuliano Antonini Department of Mathematics, University of Pisa, Pisa, 56100, Italy

Joong Sung Kwon Department of Mathematics, Sun Moon University, Asan, Chungnam, 336-840, South Korea

Soo Hak Sung Department of Applied Mathematics, Pai Chai University, Taejon, 302-735, South Korea

Andrei I. Volodin Department of Mathematics, University of Regina, Regina, Saskatchewan, Canada

Abstract

Let {X _n,n≥1} be a sequence of independent and identically distributed random variables and {a _ni,1≤i≤n,n≥1} an array of constants. Some strong convergence results for the weighted sums ∑_i=1 ⁿ a _ni X _i are obtained.

Acknowledgment

The authors S. H. Sung and J. S. Kwon were supported by Korea Research Foundation Grant (KRF-99-015-DP0044).

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On the strong convergence of weighted sums

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On the strong convergence of weighted sums

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