Optimal convergence order for multi-scale stochastic Burgers equation

In this talk, I first introduce some background of the multi-scale stochastic differential equation and related problems. Secondly, we present our main results about the strong and weak convergence orders for multi-scale one-dimensional stochastic Burgers equation. Thirdly, I show the idea of the proof, especially, the technique of how to overcome the difficulties caused from the highly nonlinear term. Finally, some further works are also introduced. This is a joint work with Peng Gao (Northeast Normal University).