Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (6): 1180-1189.

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Asymptotic Behavior of the Local Time for the Symmetric Random Walk with Stay

Sun Hongyan1, Yao Yanan2   

  1. 1 China University of Geosciences, Beijing 100081;
    2 School of Mathematical Sciences, Beijing Normal University, Beijing 100875
  • Received:2015-04-17 Revised:2015-09-23 Online:2015-12-25 Published:2015-12-25

Abstract:

We consider the symmetric random walk with stay in this paper, whose local time can be represented by a function of a non-primitive two-type branching process. Using this representation, we establish the convergence of the local time of the random walk.

Key words: Brownian local time, Random walk, Branching processes

CLC Number: 

  • O211.4
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