Acta mathematica scientia,Series B

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LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

Hu Shuhe; Wang Xuejun   

  1. School of Mathematics and Computation Science, Anhui University, Hefei 230039, China
  • Received:2005-05-05 Revised:2006-04-24 Online:2008-04-20 Published:2008-04-20
  • Contact: Hu Shuhe

Abstract:

Let (Xi) be a martingale difference sequence and Sn=∑i=1nXi. Suppose (Xi) is bounded in Lp. In the case p≥ 2, Lesigne and Volny (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation μ(Sn>n)≤ cn-p/2, Yulin Li (Statist. Probab. Lett. 62 (2003) 317) generalized the result to the case when p∈(1,2] and obtained μ(Sn>n)≤cn1-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ(Sn>n) as those for martingale difference sequence.

Key words: Large deviation, ψ-mixing sequence, NA sequence, linear process

CLC Number: 

  • 60F10
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