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

摘要

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.