In this talk, we will introduce several results on the stochastic homogenization for jump process, including the quenched invariance principle and heat kernel estimates for symmetric stable-like process on random conductance model, homogenization for non-symmetric jump process on periodic or balanced environment, stochastic homogenization for symmetric jump process on ergodic random environment. This talk is based on some joint papers with Zhen-qing Chen, Takashi Kumagai and Jian Wang.

海报