| SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK |
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| 作者姓名： | Wen Jiwei Yan Yunliang |
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| 作者单位： | [1]Dept. of Math. , Zhejiang Univ., Hangzhou 310028,China [2]Dept. of Management, Zhejiang College of Traditional Chinese Medicine, Hangzhou 310053,China. |
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| 基金项目： | Supported by the National Natural Science Foundation of China（10071072）. |
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| 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.
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| 关 键 词： | 局部时间 随机通道 精确逼近 叠对数定律 强逼近 |
| 收稿时间： | 2005-03-30 |
Some limit properties of local time for random walk |
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| Wen Jiwei Yan Yunliang.SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK[J].Applied Mathematics A Journal of Chinese Universities,2006,21(1):87-95. |
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| Authors: | Wen Jiwei Yan Yunliang |
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| Institution: | (1) Dept. of Math., Zhejiang Univ., 310028 Hangzhou, China;(2) Dept. of Management, Zhejiang College of Traditional Chinese Medicine, 310053 Hangzhou, China |
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| Abstract: | Let X, X1, X2, … be i. i. d. random variables with E
X
2+δ<∞ (for some δ>0). Consider a one-dimensional random walk S={S
n}n≥0, starting from S
0=0. Let μ*. A strong approximation of μ* 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 μ* are obtained. Furthermore, the precise asymptotics in the law of iterated logarithm of μ* is proved.
Supported by the National Natural Science Foundation of China (10071072). |
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| Keywords: | local time random walk precise asymptotic law of iterated logarithm strong approximation |
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