A random walk on Z with drift driven by its occupation time at zero

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Ben-Ari, Iddo¹  Merle, Mathieu²  Roitershtein, Alexander³ 

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Iowa State Univ, Dept Math, Ames, IA 50011 USA

关键词: Limit theorems;    Renewal theorem;    Regular variation;    Excursions of random walks;    Oscillating random walks;    Invariance principle;    Kakutani's dichotomy;   

DOI  :  10.1016/j.spa.2009.03.002

来源: Elsevier

【 摘 要 】

We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes according to the rate of decay of the drift. In particular, when the rate is sufficiently slow, the position of the random walk, properly normalized, converges to a symmetric exponential law. In this regime, in contrast to the classical case, the range of the walk scales differently from its position. Published by Elsevier B.V.

【 授权许可】

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