Acta mathematica scientia,Series B

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

Zhang Xiaomin; Hu Dihe   

  1. 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

Abstract:

Suppose {Xn} is a random walk in time-random environment with state space Zd, |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.

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

CLC Number: 

  • 60J15
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