Abstract:

Let (X_i) be a martingale difference sequence and S_n=∑_i=1ⁿX_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)≤ cn^-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)≤cn^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.

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