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| THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS | |
| 作者姓名： | 张晓敏 胡迪鹤 |
| 作者单位： | Faculty of Science Ningbo University Ningbo 315211，China，School of Mathematics and Statistics Wuhan University，Wuhan 430072，China |
| 基金项目： | Project supported by NNSF of China (10371092)，Foundation of Wuhan University |
| 摘 要： | 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 a. 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： | 离散分形 Hausdorff量纲 密实度量纲 随机通道 |
| 收稿时间： | 2004-06-09 |
THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS |
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| Xiaomin Zhang,Dihe Hu,.THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS[J].Acta Mathematica Scientia,2006,26(4):615-628. | |
| Authors: | Xiaomin Zhang Dihe Hu |
| Institution: | aFaculty of Science, Ningbo University, Ningbo 315211, China bSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
| 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 a. 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. |
| Keywords: | Random walks in time-random environments discrete fractal Hausdorff dimension Packing dimension |
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