Large deviations viewpoints for a heavy-tailed β-mixing sequence  

作　　者：LIU Yan HU Yijun 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

出　　处：《Science China Mathematics》2005年第11期1554-1566,共13页中国科学：数学（英文版）

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.10071058,70273029);the Ministry of Education of China.

摘　　要：Let (Xn;n≥1) be a stationary sequence of non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the distributions of the partial sums sn=X1+X2+…+Xn. We obtain the crude estimates P(Sn>nx)≈n-αx+1 for appropriate values of x, where a is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.Let {Xn; n ≥ 1} be a stationary sequenceof non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the disp(Sn ＞ nx) ≈ n-αx+1 for appropriate values of x, where α is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.

关 键 词：logarithmic asymptotics large deviations heavy tails mixing 

分 类 号：N[自然科学总论]