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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
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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 >.
机构地区 浙江大学数学系
出处 《数学年刊(A辑)》 CSCD 北大核心 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.
关键词 主值 局部时 随机游动 Baum—Katz律 Davis律 Principal value, Local time, Random walk, Baum-Katz law, Davis law
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参考文献14

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