Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn ...Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. 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） ≤ cn^l-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.展开更多
Let {ζ,-co 〈 i 〈 ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables with zero means and finite variances, {ai, -∞〈 i 〈 ∞} be an absolutely summable sequence of real numbers ...Let {ζ,-co 〈 i 〈 ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables with zero means and finite variances, {ai, -∞〈 i 〈 ∞} be an absolutely summable sequence of real numbers and Xk = ∑＋∞ i=-∞ ai{ζi＋k be a moving average process. Under some proper moment conditions, the precise asymptotics are established for展开更多
I. INTRODUCTION AND SOME LEMMASLet{ε<sub>i</sub>} be independent random variables, E（ε<sub>i</sub>） = 0, E（ε<sub>i</sub><sup>2</sup>） =σ<sup>2</sup>,...I. INTRODUCTION AND SOME LEMMASLet{ε<sub>i</sub>} be independent random variables, E（ε<sub>i</sub>） = 0, E（ε<sub>i</sub><sup>2</sup>） =σ<sup>2</sup>, sup E[ε<sub>i</sub>|<sup>r</sup>【∞ for some r】2, {a<sub>ni</sub>} be a double array of constants satisfying proper conditions. Ref. [1] gave展开更多
基金the National Natural Science Foundation of China(10571001)the Innovation Group Foundation of Anhui University
文摘Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. 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） ≤ cn^l-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.
基金Supported by National Science Foundation of China (Grant No. 11171303)Specialized Research Fund for Doctor Program of Higher Education (Grant No. 20090101110020)Foundation of Zhejiang Educational Committee (Grant No. Y201120141)
文摘Let {ζ,-co 〈 i 〈 ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables with zero means and finite variances, {ai, -∞〈 i 〈 ∞} be an absolutely summable sequence of real numbers and Xk = ∑＋∞ i=-∞ ai{ζi＋k be a moving average process. Under some proper moment conditions, the precise asymptotics are established for
基金Project supported by the National Youth Natural Science Foundation of China.
文摘I. INTRODUCTION AND SOME LEMMASLet{ε<sub>i</sub>} be independent random variables, E（ε<sub>i</sub>） = 0, E（ε<sub>i</sub><sup>2</sup>） =σ<sup>2</sup>, sup E[ε<sub>i</sub>|<sup>r</sup>【∞ for some r】2, {a<sub>ni</sub>} be a double array of constants satisfying proper conditions. Ref. [1] gave
