Some Properties Of A Class Of Hybrid Stable Processes

This paper mainly studies a class of multidimensional hybrid stochastic population models driven by -stable processes.First of all,we prove that the harmonic function corresponding to the solution of the hybrid stable process satisfies the maximum theorem.Besides,Harnack inequality and the comparison theorem corresponds to stable processes with Markov switching is given.Finally,we give the sufficient conditions for the solution process of the studied model to have a unique stationary distribution.In the meanwhile,existence and uniqueness for global positive solution,extinction and positive recurrence of the model are given.The sufficient conditions for ergodicity of the model are discussed when the parameter α→ 2.