两类带渐近扰动的随机过程的若干性质

Some properties of two classes of stochastic processes with asymptotic perturbation

本文考虑两类带渐近扰动的随机模型.一类是带渐近扰动的非紧邻随机游动,考虑其常返暂留性,并给出该模型正常返性的判别.另一类是带渐近扰动的随机环境中分枝过程,通过分析其相关随机游动的极限行为,给出分枝过程灭绝和不灭绝的判别条件.

In this paper, we consider two kinds of stochastic models with asymptotic perturbation. One is the non-nearest neighbor random walk with asymptotic perturbation, for which we consider the transience and recurrence of the random walk. We give the criterion for positive recurrent of the random walk. The other is the branching process in random environment with asymptotic perturbation, for which by analyzing the limit behavior of the associated random walk, we give the criterion of extinction and non-extinction of the branching process.