Homogenization of Symmetric Stable-like Processes in Stationary Ergodic Media
Xin Chen, Zhen-Qing Chen, Takashi Kumagai, Jian Wang · SIAM Journal on Mathematical Analysis · 2021
This paper studies homogenization of symmetric nonlocal Dirichlet forms with stable-like jumping kernels in a one-parameter stationary ergodic environment. Under suitable conditions, we establish results of homogenization and identify the limiting effective Dirichlet forms explicitly. The coefficients in the jumping kernels of Dirichlet forms and symmetrizing measures are allowed to be degenerate and unbounded, and the coefficients in the effective Dirichlet forms can also be degenerate.