Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664765 | Acta Mathematica Scientia | 2006 | 14 Pages |
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.
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