SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK  

作　　者：Wen Jiwei Yan Yunliang 

机构地区：[1]Dept. of Math. , Zhejiang Univ., Hangzhou 310028,China [2]Dept. of Management, Zhejiang College of Traditional Chinese Medicine, Hangzhou 310053,China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2006年第1期87-95,共9页高校应用数学学报（英文版）（B辑）

基　　金：SupportedbytheNationalNaturalScienceFoundationofChina(10071072).

摘　　要：Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.

关 键 词：local time random walk precise asymptotic law of iterated logarithm strong approximation. 

分 类 号：O241.5[理学—计算数学]