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

doi:10.1016/S0252-9602(06)60088-X

数学物理学报(英文版)

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

张晓敏; 胡迪鹤

宁波大学理学院, 宁波 315211

收稿日期:2004-06-09 修回日期:1900-01-01 出版日期:2006-10-20 发布日期:2006-10-20
通讯作者: 张晓敏
基金资助:
Project supported by NNSF of China (10371092) and Foundation of Wuhan University

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

Zhang Xiaomin; Hu Dihe

Faculty of Science, Ningbo University, Ningbo 315211, China

Received:2004-06-09 Revised:1900-01-01 Online:2006-10-20 Published:2006-10-20
Contact: Zhang Xiaomin

摘要/Abstract

摘要：

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

关键词: Random walks in time-random environments, discrete fractal, Hausdorff dimension, Packing dimension

Abstract:

Key words: Random walks in time-random environments, discrete fractal, Hausdorff dimension, Packing dimension

中图分类号:

60J15

张晓敏; 胡迪鹤. THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS[J]. 数学物理学报(英文版), 2006, 26(4): 615-628.

Zhang Xiaomin; Hu Dihe. THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS[J]. Acta mathematica scientia,Series B, 2006, 26(4): 615-628.

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

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

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