Central limit theorems for biased randomly trapped random walks on Z

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Bowditch, Adam¹ 

[1] Univ Warwick, Warwick, England

关键词: Random walk;    Random environment;    Randomly trapped;    Galton-Watson tree;    Annealed;    Quenched;    Functional central limit theorem;    Invariance principle;   

DOI  :  10.1016/j.spa.2018.03.017

来源: Elsevier

【 摘 要 】

We prove CLTs for biased randomly trapped random walks in one dimension. By considering a sequence of regeneration times, we will establish an annealed invariance principle under a second moment condition on the trapping times. In the quenched setting, an environment dependent centring is necessary to achieve a central limit theorem. We determine a suitable expression for this centring. As our main motivation, we apply these results to biased walks on subcritical Galton-Watson trees conditioned to survive for a range of bias values. (C) 2018 The Author. Published by Elsevier B.V.

【 授权许可】

Free