SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2957-3001, January 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.

中文翻译：

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平稳遍历介质中对称稳定过程的均质化

SIAM数学分析杂志，第53卷，第3期，第2957-3001页，2021年1月。
本文研究在单参数平稳遍历环境中对称非局部Dirichlet形式与稳定类跳跃核的均质化。在合适的条件下，我们确定均质化的结果，并明确确定有效的狄利克雷极限形式。Dirichlet形式和对称度量的跳跃核中的系数可以退化和无界，有效Dirichlet形式中的系数也可以退化。