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›› 2017, Vol. 34 ›› Issue (1): 1-7.DOI: 10.7523/j.issn.2095-6134.2017.01.001

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Classification of states for a biased random walk on a branching tree in the varying environment

ZHANG Zhiyang, HU Xiaoyu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-12-30 Revised:2016-05-20 Online:2017-01-15

Abstract:

In this study we investigate biased random walk on branching trees in the varying environment. We have obtained the sufficient conditions for transience, positive recurrence, and null recurrence. Our main result enables the further study on the central limit theory for this kind of random walks.

Key words: random walk on a tree, branching process in the varying environment, recurrence, transience

CLC Number: