Date of Award

May 2021

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Chao Zhu

Committee Members

Suzanne Boyd, Richard Stockbridge, Jeb Willenbring, Wei Wei


exponential ergodicity, Feller property, Foster-Lyapunov function, irreducibility, regime-switching jump diffusion, strong Feller property


This work is devoted to the study of regime-switching jump diffusion processes in which the switching component has countably infinite regimes. Such processes can be used to model complex hybrid systems in which both structural changes, small fluctuations as well as big spikes coexist and are intertwined. Weak sufficient conditions for Feller and strong Feller properties and irreducibility for such processes are derived; which further lead to Foster-Lyapunov drift conditions for exponential ergodicity. Our results can be applied to stochastic differential equations with non-Lipschitz coefficients. Finally, an application to feedback control problems is presented.

Included in

Mathematics Commons