Complete moment convergence of moving average processes under ρ-mixing assumption

Mathematica Slovaca - Tập 61 - Trang 979-992 - 2011
Xing-Cai Zhou1,2, Jin-Guan Lin1
1Department of Mathematics, Southeast University, Nanjing, Jiangsu, China
2Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui, China

Tóm tắt

Let {Y i : −∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, and {a i : −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper we prove the complete moment convergence for the partial sums of moving average processes $\{ X_n = \sum\limits_{i = - \infty }^\infty {a_i Y_{i + n,} n \geqslant 1} \} $ based on the sequence {Y i : −∞ < i < ∞} of ρ-mixing random variables under some suitable conditions.

Tài liệu tham khảo

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