Homogenization of symmetric stable-like processes in stationary ergodic media

Xin Chen; Zhen Qing Chen; Takashi Kumagai; Jian Wang

doi:10.1137/20M1326726

Homogenization of symmetric stable-like processes in stationary ergodic media

Xin Chen, Zhen Qing Chen, Takashi Kumagai, Jian Wang

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2957-3001
Number of pages	45
Journal	SIAM Journal on Mathematical Analysis
Volume	53
Issue number	3
DOIs	https://doi.org/10.1137/20M1326726
Publication status	Published - 2021
Externally published	Yes

Keywords

Ergodic random medium
Homogenization
Symmetric nonlocal Dirichlet form
α-stable-like operator

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10.1137/20M1326726

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Chen, X., Chen, Z. Q., Kumagai, T., & Wang, J. (2021). Homogenization of symmetric stable-like processes in stationary ergodic media. SIAM Journal on Mathematical Analysis, 53(3), 2957-3001. https://doi.org/10.1137/20M1326726

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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",

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AU - Chen, Xin

AU - Chen, Zhen Qing

AU - Kumagai, Takashi

AU - Wang, Jian

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Ergodic random medium

KW - Homogenization

KW - Symmetric nonlocal Dirichlet form

KW - α-stable-like operator

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DO - 10.1137/20M1326726

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EP - 3001

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

Homogenization of symmetric stable-like processes in stationary ergodic media

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Keywords

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