The precise asymptotics of the complete convergence for moving average processes of <Emphasis Type="Italic">m</Emphasis>-dependent <Emphasis Type="Italic">B</Emphasis>-valued elements期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The precise asymptotics of the complete convergence for moving average processes of <Emphasis Type="Italic">m</Emphasis>-dependent <Emphasis Type="Italic">B</Emphasis>-valued elements

Authors:	Xi Li Tan Xiao Yun Yang

Institution:	(1) Institute of Mathematics, Beihua University, Jilin, 132013, P. R. China;(2) Institute of Mathematics, Jilin University(Qianwei Campus), Changchun, 130012, P. R. China

Abstract:	Let {⃛ _t; t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a_j; j ∈ Z} is a sequence of real numbers satisfying $\sum\nolimits_{j = - \infty }^\infty {\left\| {a_j } \right\|} < \infty$ . Define a moving average process $X_t = \sum\nolimits_{j = - \infty }^\infty {a_{j + t} \varepsilon _j ,t \geqslant 1}$ , and $S_n = \sum\nolimits_{t = 1}^n {X_t ,n \geqslant 1}$ . In this article, by using the weak convergence theorem of $\{ \frac{{S_n }} {{\sqrt n }};n \geqslant 1\}$ , we study the precise asymptotics of the complete convergence for the sequence {X _t; t ∈ N}. Research supported by National Natural Science Foundation of China (No. 10571073)

Keywords:	m-dependent random element moving average process complete convergence precise asymptotics
本文献已被维普 SpringerLink 等数据库收录！