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