JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (11): 119-126.doi: 10.6040/j.issn.1671-9352.0.2014.596

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A class of random walks in a random environment with singular jumps

FEI Shi-long1, BAI Yao-qian2   

  1. 1. School of Mathematics and Statistics, Suzhou University, Suzhou 234000, Anhui, China;
    2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Received:2014-12-31 Revised:2015-07-22 Online:2015-11-20 Published:2015-12-09

Abstract: A class of random walks on half-line in a random environment with singular jumps were introduced, which promoted a case of random walks on half-line in a random environment with nearest-neighbor or bounded jumps. First of all, several sufficient and necessary conditions that recurrence and transience criteria of states were obtained by using suitable inequality and recurrence and transience criteria of Markov chains when the environment was fixed. Furthermore several criteria about positive recurrence and null recurrence of states were discussed assuming that the state was recurrent. At last assuming the environment is a sequences of random variables, the recurrence and transience criteria and criteria of positive recurrence and null recurrence were obtained by using the limit theory of random variables. These conclusions are the promotion of some results of other papers.

Key words: transience, positive recurrence, random walks, random environments, null recurrence, recurrence

CLC Number: 

  • O211.62
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