Stochastic processes and stochastic equations:
I focus on the SDEs (Stochastic differential equations), SDDEs (stochastic delay differential equations), SFDEs (Stochastic functional differential equations), SPDEs (stochastic partial differential equations), which are mainly motivated from applications such as biology, ecology, physics and among others.
The properties I mainly studied of these equations conclude: ergodicity, stationary distribution, stability and limit behaviors such as: averaging principle, large deviation principle.
Related Publications:
Stability and Stabilization of Coupled Jump Diffusions and Applications (with D. Nguyen, Duy Nguyen, G. Yin), submitted. [arXiv]
Stability of Stochastic Functional Differential Equations with Random Switching and Applications (with N. Du, D. Nguyen, G. Yin), Automatica, Vol. 125 (2021), 109410. [Journal] [pdf]