Properties And Statistical Inference Of Two Types Of Hybrid Models

This paper focuses on long time behavior for two types of hybrid models and their parameter estimation problems.First of all,this paper studies the stability and ergodicity of a class of linear hybrid diffusion models.Based on the Khasminskii type lemma,we provide some sufficient conditions for ergodicity of OU type SDE driven by stable processes.Then,some sufficient conditions for stablity of geometrically stable type SDE are given.Next,consider the stopping time problems and related properties of a class of hybrid diffusion models dXt=μrtXtdt+σrtdWt driven by Brownian motion.The problem is transformed into a quadratic eigenvalue solution using infinitesimal generating elements of Markov chains.Some explicit expressions for the mean exit time,the escape probability,and the Laplace transform of the mean exit time for the hybrid process are provided at some cases.In particular,some explicit expressions for the mean exit time of the switching Brownian motion with N+1 states are given for some special transition rate matrices Q.In the last chapter,some expressions of the parameter estimators of Brownian motion-driven hybrid model are given by the EM algorithm.Besides,we provide the implicit state estimation of the Markov chain.Finally,we prove that the estimators converge in probability.Some examples are provided to illustrate our results.