Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (5): 1210-1241.

• Articles • Previous Articles     Next Articles

An Introduction to Markov Process in Random Environment

 HU Di-He   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2010-01-08 Revised:2010-04-08 Online:2010-10-25 Published:2010-10-25
  • Supported by:

    国家自然科学基金(10771185)资助

Abstract:

We will introduce some results on Markov processes in random environments in this paper, there are four chapters in it. In chapter 1, we introduce the Markov chains in time random environments, including existence and equivalence; the chassification of states, ergodic theory and invariant measure, the central limit theorem and invariance principle for p-θ chain. In chapter 2, we introduce the Markov processes in time random environments, including some basic concepts, the exsistence and uniqueness for q-process in random environment, homogenious q-q-processes in random environments, the construction theorem and equivalence. In chapter 3 we introduce the branching chains in time random environments, including the models for finite dimension and infinite dimension, the extinction probability and palarization and
proliferattion rate are introduced. In chapter 4, we introduce the Markov chains in space time random environments, including basic concepts, central limit theorem and invariance priciple for RWSTRE.

Key words: Markov chains in time random environments, Markov chains in space time random environments, Markov processes in time random environments, Branching chains in random environments, Random walks in space time random environments

CLC Number: 

  • 60J05
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