Escape And Quasipotential Problems Of Markov Chains With Exponential Perturbations

This paper mainly studies the escape,stationary distribution,pseudo-potential,and the simplification of pseudo-potentials of the Markov chain with exponential per-turbations.The first chapter introduces the research background,research status and main re-search contents,and introduces the basic concepts and related properties of the Markov chain with exponential perturbation,which provides a theoretical basis for the later re-search work.The second chapter mainly makes appropriate deformations for some basic defi-nitions under discrete time conditions,and changes the discrete time in the document Chen-Feng-Qian(1995a)to continuous time,and proves some important lemmas(such as probability of first arrival,time of first departure).Then proceed from the lemma and definition,explore the continuous time Markov chain's first time of departure,also the first departure distribution and so on.It is concluded that the first departure time and the first departure distribution are determined by quasipotential,and eventually we'v got the relational expression between them.The third chapter studies the relationship between the stationary distribution and T*(Bi)when the continuous time Markov chain with exponential perturbation has a stationary distribution.The fourth chapter studies whether the quasipotential T(Bi)of the discrete-time Markov chain with exponential perturbation can be simplified.Due to the abstractness of the definition of T(Bi)in Chen-Feng-Qian(1995a),we cannot comprehend T(Bi)well,so it is expected to simplify quasipotential and get an explicit expression of it.In the article Chen-Feng-Qian(1997a),the inversion of the I sing model is used to ob-tain the conclusion that quasipotential can be fully characterized by the Halmiton.This article is generalized on this basis,considering the Markov chain to be path-independent,thus generating energy function.At this time,the quasipotential T(Bi)is path-independent,and finally the expression of the relationship between T(Bi)and the energy function is obtained.