Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 5: 1033 - 1044

DOI: https://doi.org/10.1007/s11464-018-0723-y

RESEARCH ARTICLE

Scaling limit theorem for transient random walk in random environment

  • Wenming HONG 1 ,
  • Hui YANG , 2
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  • 1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China
  • 2. College of Science, Minzu University of China, Beijing 100081, China

Received date: 09 Jun 2016

Accepted date: 11 Aug 2018

Published date: 29 Oct 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We construct a sequence of transient random walks in random environments and prove that by proper scaling, it converges to a diffusion process with drifted Brownian potential. To this end, we prove a counterpart of convergence for transient random walk in non-random environment, which is interesting itself.

Key words： Random walk; random environment; diffusion process; Brownian motion with drift

Cite this article

Wenming HONG , Hui YANG . Scaling limit theorem for transient random walk in random environment[J]. Frontiers of Mathematics in China, 2018 , 13(5) : 1033 -1044 . DOI: 10.1007/s11464-018-0723-y

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