DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Hongjian Qian (Auburn University)

Title: Moderate Deviation Principles for Stochastic Differential Equations in Fast-Varying Markovian Environment

Abstract: In this talk, we will show moderate deviation principles for a fully coupled two-time-scale stochastic system. The slow process is governed by stochastic differential equations with small noise, while the fast process is a rapidly changing purely jump process on finite state space. The system is fully coupled in that the drift and diffusion coefficients of the slow process, as well as the jump distribution of the fast process, depend on states of both processes. The diffusion component may be degenerate. Our approach is based on the combination of the weak convergence method from [A. Budhiraja, P. Dupuis, and A. Ganguly, Electron. J. Probab. 23 (2018), pp. 1-33; Ann. Probab. 44 (2016), pp. 1723-1775] with the Poisson equation for the fast-varying purely jump process.

Host: Le Chen