THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a...

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Bibliographic Details
Published inActa Mathematica Scientia Vol. 26; no. 4; pp. 615 - 628
Main Author 张晓敏 胡迪鹤
Format Journal Article
LanguageEnglish
Published Faculty of Science, Ningbo University, Ningbo 315211, China%School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 01.10.2006
Subjects
Hausdorff量纲
密实度量纲
离散分形
随机通道
Random walks in time-random environments
discrete fractal
Hausdorff dimension
Packing dimension
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Summary:Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.
Bibliography:Random walks in time-random environments, discrete fractal, Hausdorff dimension, Packing dimension
O411
42-1227/O
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0252-9602
1572-9087
1003-3998
DOI:10.1016/S0252-9602(06)60088-X