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Speaker: Chao Zhu (University of Wisconsin-Milwaukee)

Abstract: This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),\Lambda(t))$, where the analog component $X(t) \in R^{d}$ models the state of interest while the switching component $\Lambda(t)\in \{1,2,\dots\}$ can be used to describe the structural changes of the state or random factors that are not represented by the usual jump diffusion formulation. Considering the corresponding stochastic differential equations, our focus is on treating those with non-Lipschitz coefficients. We first show that there exists a unique strong solution to the corresponding stochastic differential equation. Then Feller and strong Feller properties and exponential ergodicity are investigated. This is a joint work with Khwanchai Kunwai, Fubao Xi and George Yin.