Regime-Switching Jump Diffusion Processes with Countable Regimes: Feller, Strong Feller, Irreducibility and Exponential Ergodicity
Date of Award
Doctor of Philosophy
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.
Kunwai, Khwanchai, "Regime-Switching Jump Diffusion Processes with Countable Regimes: Feller, Strong Feller, Irreducibility and Exponential Ergodicity" (2021). Theses and Dissertations. 2685.