Acta mathematica scientia,Series B
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Hu Shuhe; Wang Xuejun
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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
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Hu Shuhe; Wang Xuejun. LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES[J].Acta mathematica scientia,Series B, 2008, 28(2): 295-300.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(08)60030-2
http://121.43.60.238/sxwlxbB/EN/Y2008/V28/I2/295
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