局部时的Cauchy主值的精确完全收敛性  

PRECISE ASYMPTOTICS IN THE BAUM-KATZ AND DAVIS LAWS OF LARGE NUMBERS OF CAUCHY'S PRINCIPAL VALUES RELATED TO LOCAL TIME

作　　者：黄炜 张立新[1] 闻继威[1] 

机构地区：[1]浙江大学数学系,杭州310028

出　　处：《数学年刊（A辑）》2004年第5期587-600,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10071072)资助的项目.

摘　　要：设{X,Xn;n≥1)为i.i.d.的随机变量序列,其均值为0且EX2=1.令S={Sn}n≥0为一维随机游动,其中S0=0,Sn=sum from k=1 to n Xk,对n≥1.定义G(n)为随机游动局部时的Cauchy主值.本文得到了,若存在某δ1>0,E|X|2r/(3p-4)+δ1<∞成立,那么对4/3<P<2及r>P。Let {X, Xn; n ≥1} be a sequence of i.i.d. random variables with EX = 0 and EX2 = 1. And let S = {Sn}n≥0 be a one-dimensional random walk, where S0 = 0 and Sn = sum from k=1 to n Xk, n≥1. Define G(n) to be the Cauchy's principal value of random walk local time. Then, for 4/3 < p < 2 and r >, if E|X|2r/(3p-4)+δ1 <∞, for some δ1 >.

关 键 词：主值 局部时 随机游动 Baum—Katz律 Davis律 

分 类 号：O212[理学—概率论与数理统计]