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 t...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.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.10071058,70273029)the Ministry of Education of China.
文摘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.
