@article{8474c4b8abd245899921a0ca058d8958,
title = "Homogenization of symmetric stable-like processes in stationary ergodic media",
abstract = "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.",
keywords = "Ergodic random medium, Homogenization, Symmetric nonlocal Dirichlet form, α-stable-like operator",
author = "Xin Chen and Chen, {Zhen Qing} and Takashi Kumagai and Jian Wang",
note = "Funding Information: ∗Received by the editors March 23, 2020; accepted for publication (in revised form) February 22, 2021; published electronically May 20, 2021. https://doi.org/10.1137/20M1326726 Funding: The work of the first author was supported by the National Natural Science Foundation of China grant 11871338. The work of the second author was partially supported by the Simons Foundation grant 520542 and a Victor Klee Faculty Fellowship at the University of Washington. The work of the third author was supported by the JSPS KAKENHI grant JP17H01093 and by the Alexander von Humboldt Foundation. The work of the fourth author was supported by the National Natural Science Foundation of China grants 11831014 and 12071076, the Program for Probability and Statistics: Theory and Application (IRTL1704), and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics.",
year = "2021",
doi = "10.1137/20M1326726",
language = "English",
volume = "53",
pages = "2957--3001",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}