ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES
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Let {Yi;−∞ < i < ∞} be a doubly infinite sequence of identically distributed and ρ*-mixing random variables with zero means and finite variances and {ai;−∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {수식} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191–197.] to the ρ*-mixing case.
Abstract
Let {Yi;−∞ < i < ∞} be a doubly infinite sequence of identically distributed and ρ*-mixing random variables with zero means and finite variances and {ai;−∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {수식} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191–197.] to the ρ*-mixing case.
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