Two Classes Of Hybrid Systems And Their Applications

In this paper,we study two classes of diffusion systems with Markov switching.First of all,by solving the corresponding Poisson equations,some estimated solution of the escape probability and the mean exit time of hybrid OU process are obtained.Then,the parameter estimation algorithm of the hybrid OU process is given by the composite maximum likelihood method and the EM algorithm.Besides,by diagonalizing the covariance matrix,the parameters of two classes of differential equations driven by fractional Brownian motion are estimated by the EM algorithm.Finally,several examples are given to illustrate our results.