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A general result on precise asymptotics for linear processes of positively associated sequences

Authors:	Xi-li Tan Xiao-yun Yang

Institution:	(1) Dept. of Math., Beihua Univ., Jilin, 132013, China;(2) Institute of Math., Jilin Univ.(Qianwei Campus), Changchun, 130012, China

Abstract:	Let {ε _t; t ∈ Z ⁺} be a strictly stationary sequence of associated random variables with mean zeros, let 0 < Eε ₁ ² < ∞ and $\sigma ^2 = E\varepsilon _1^2 + 2\sum\limits_{j = 2}^\infty {E\varepsilon _1 \varepsilon _j }$ with 0 < σ ² < ∞. {a _j; j ∈ Z ⁺} is a sequence of real numbers satisfying $\sum\limits_{j = 0}^\infty {\left\| {a_j } \right\| < \infty }$ . Define a linear process $X_t = \sum\limits_{j = 0}^\infty {a_j \varepsilon _{t - j} ,t \geqslant 1}$ , and $S_n = \sum\limits_{t = 1}^n {X_t ,n \geqslant 1}$ . Assume that E\|ε₁\|^2+δ′ < ∞ for some δ′ > 0 and μ(n) = O(n ^−ρ) for some ρ > 0. This paper achieves a general law of precise asymptotics for {S _n}. Supported by the National Natural Science Foundation of China(10571073).

Keywords:	PA sequence linear process general law precise asymptotics
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