Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1669-1678.doi: 10.1016/S0252-9602(10)60160-9

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THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT (I): MODEL, MARKOV PROPERTY, MOMENTS

 HU Di-He, HU Xiao-Yu   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2008-03-05 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    Supported by the NSFC (10371092, 11771185, 10871200).

Abstract:

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE),  i.e.,  the coupling of branching chain and random walk. In Section 2,  we prove that any BCDSTRE must be a Markov chain in
time random environment when we consider the distribution of the particles in space as a random element. In Section 3,  we calculate the first-order moments and the second-order moments of BCDSTRE.

Key words: branching chain with drift in space-time random environment, random branching generating function,  local random transition generating function, random drift law, random branching law

CLC Number: 

  • 60J27
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