Behavior of Multi-Scale SDEs with State-Dependent Switching

2023.12.15 15:00 N613 

In this talk, we discuss the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov chain and the regularity of its solutions. As applications of the results on Poisson equations, we prove five types of convergence, more precisely, three averaging principle results and two central limit theorems results. The achieved convergence orders are all proven to be optimal through several examples. This talk is based on a joint work with Professor Yingchao Xie.