COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM VARIABLES(II)

  • Sung, Soo-Hak (Department of Applied mathematics, Pai Chai University)
  • Published : 2000.05.01

Abstract

Let ${X_{nk}}, u_n\; \leq \;k \leq \;u_n,\; n\; \geq\; 1}$ be an array of rowwise independent, but not necessarily identically distributed, random variables with $EX_{nk}$=0 for all k and n. In this paper, we povide a domination condition under which ${\sum^{u_n}}_=u_n\; S_{nk}/n^{1/p},\; 1\; \leq\; p\;<2$ converges completely to zero.

Keywords

complete convergence;arrays;rowwise independent random variables;moving average

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