Averaging Principle and Large Deviation for Multiple Time-Scale Switching Processes

Speaker: Jinghai Shao (Tianjin University)

Date: May 15 Sun. 2:30pm

Venue: Tencent Meeting Room: 436 702 636

Abstract: We investigate a system with two time-scales. The slow-scale system is described by a diffusion processes with small noise whose drifts and diffusion coefficients both depend on a fast-scale process. The fast-scale process is a continuous time jumping process on a finite state space, whose transition rates may depend on the slow-scale component. The slow-scale system approximates a deterministic dynamic system by averaging over the fast component. In this work we first provide conditions so that the averaging principle holds via a coupling method. Then, the large deviation principle is established using the nonlinear semigroup approach under two different slow-fast time-scale orders.