Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the int...Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the integral test for the weighted partial sums {Σi=1naniXi,n ≥ 1}, and obtain the Chover's laws of iterated logarithm(LIL) as corollaries.展开更多
Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probabil...Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.展开更多
Let Y={Y_n;n∈N^2} be a stationary linear random field generated by a two- dimensional martingale difference. Where N^2 denotes the two dimensional integer lattice. The main purpose of this paper is to obtain the LIL ...Let Y={Y_n;n∈N^2} be a stationary linear random field generated by a two- dimensional martingale difference. Where N^2 denotes the two dimensional integer lattice. The main purpose of this paper is to obtain the LIL convergence for the partial-sums of Y.展开更多
基金Supported by the National Natural Science Foundation of China (10271120)
文摘Let {Xn,n ≥ 1} be a sequence of α-stable random variables(0 < α < 2), {ani,1 ≤ i≤ n, n≥1} be an array of constant real numbers. Under some restriction of {ani,1 ≤ i ≤ n,n≥1}, the authors discuss the integral test for the weighted partial sums {Σi=1naniXi,n ≥ 1}, and obtain the Chover's laws of iterated logarithm(LIL) as corollaries.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901138,11071213,11026087)supported by National Natural Science Foundation of China (Grant No.11071214)+1 种基金Natural Science Foundation of Zhejiang Province (Grant No.R6100119)Program for New Century Excellent Talents in University
文摘Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.
文摘Let Y={Y_n;n∈N^2} be a stationary linear random field generated by a two- dimensional martingale difference. Where N^2 denotes the two dimensional integer lattice. The main purpose of this paper is to obtain the LIL convergence for the partial-sums of Y.
