Abstract
Let { X n i , i ≥ 1 , n ≥ 1 } Open image in new window be an array of rowwise ρ ˜ Open image in new window-mixing random variables. Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ ˜ Open image in new window-mixing random variables are presented without assumptions of identical distribution. As applications, the Baum and Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of ρ ˜ Open image in new window-mixing random variables are obtained.
Highlights
The concept of complete convergence was introduced by Hsu and Robbins [ ] as follows
The main purpose of this paper is to further study the complete convergence for weighted sums of arrays of rowwise ρ-mixing random variables under mild conditions
We give some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ-mixing random variables without assumption of identical distribution
Summary
The main purpose of the paper is to provide complete convergence for weighted sums of arrays of rowwise ρ-mixing random variables. An and Yuan [ ] obtained a complete convergence result for weighted sums of identically distributed ρ-mixing random variables as follows. ) does not exist and obtained a new complete convergence result for weighted sums of identically distributed ρ-mixing random variables as follows.
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