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

被引：0
|
作者：
张晓敏
胡迪鹤
机构：
[1] Faculty of Science Ningbo University Ningbo 315211
[2] China
[3] School of Mathematics and Statistics Wuhan University
[4] Wuhan 430072
来源：
ActaMathematicaScientia | 2006年 / 04期
关键词：
Random walks in time-random environments; discrete fractal; Hausdorff dimension; Packing dimension;
D O I：
暂无
中图分类号：
O211.6 [随机过程];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码：615 / 628
页数：14
相关论文
共 50 条
  • [21] RANDOM-WALKS IN RANDOM-ENVIRONMENTS
    FISHER, DS
    PHYSICAL REVIEW A, 1984, 30 (02): : 960 - 964
  • [22] A COMPARISON OF RANDOM WALKS IN DEPENDENT RANDOM ENVIRONMENTS
    Scheinhardt, Werner R. W.
    Kroese, Dirk P.
    ADVANCES IN APPLIED PROBABILITY, 2016, 48 (01) : 199 - 214
  • [23] Fluctuations of random walks in critical random environments
    Mardoukhi, Yousof
    Jeon, Jae-Hyung
    Chechkin, Aleksei, V
    Metzler, Ralf
    PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2018, 20 (31) : 20427 - 20438
  • [24] A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
    Rezakhanlou, F.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2011, 37 (02): : 5 - 20
  • [25] Random walks in random environments on metric groups
    Rozikov, UA
    MATHEMATICAL NOTES, 2000, 67 (1-2) : 103 - 107
  • [26] Random Walks in Random Environments in the Perturbative Regime
    Zeitouni, Ofer
    NEW TRENDS IN MATHEMATICAL PHYSICS, 2009, : 823 - 826
  • [27] Some Probability Properties of Random Walk in Time-Random Environment
    Zhang Xiao-min
    WuhanUniversityJournalofNaturalSciences, 2004, (02) : 139 - 143
  • [28] Asymptotic direction for random walks in random environments
    Simenhaus, Francois
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2007, 43 (06): : 751 - 761
  • [29] Collisions of random walks in dynamic random environments
    Halberstam, Noah
    Hutchcroft, Tom
    ELECTRONIC JOURNAL OF PROBABILITY, 2022, 27
  • [30] Random walks in random environments on metric groups
    U. A. Rozikov
    Mathematical Notes, 2000, 67 : 103 - 107
12345