胡舒合; 王学军
Hu Shuhe; Wang Xuejun
摘要:
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.
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