The branching chain with drift in space-time random environment (I): Model,Markov property,moments |
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Authors: | Hu Dihe Hu Xiaoyu |
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Institution: | 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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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. |
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Keywords: | branching chain with drift in space-time random environment random branching generating function local random transition generating function random drift law random branching law |
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