HOMOGENIZATION OF SYMMETRIC JUMP PROCESSES IN RANDOM MEDIA

被引：0

作者：

Chen, Xin ^{[1
]}

Chen, Zhen-Qing ^{[2
]}

Kumagai, Takashi ^{[3
]}

Wang, Jian ^{[4
,5
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

[3] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[4] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Peoples R China

[5] Fujian Normal Univ, Ctr Appl Math Fujian Prov FJNU, Fuzhou 350007, Peoples R China

来源：

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES | 2021年 / 66卷 / 01期

基金：

中国国家自然科学基金;

关键词：

homogenization; symmetric non-local Dirichlet form; stationary er-godic environment; alpha-stable-like operator; STOCHASTIC HOMOGENIZATION; PERIODIC HOMOGENIZATION; INVARIANCE-PRINCIPLE; DIFFUSIONS; DEGENERATE; OPERATORS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper surveys some recent progress in [8] for the study of homogenization of symmetric jump processes in a one-parameter stationary ergodic environment. We further present some additional homogenization results under assumptions that are variants of [8], and identify the limiting effective Dirichlet forms explicitly. The jumping kernels of Dirichlet forms are of ca-stable-like with 0 < alpha < 2, and the associated coefficients as well as the coefficients of symmetrizing measures are allowed to be degenerate and unbounded.

引用

页码：83 / 105

页数：23

共 37 条

[1]

Allaire G., 2002, SHAPE OPTIMIZATION H, V1st ed.

[2]

[Anonymous], 2012, Fluctuations in Markov Processes: Time Symmetry and Martingale Approximation

[3]

[Anonymous], STOCHASTIC DIFFERENT, DOI DOI 10.1007/978-1-4612-1592-9_3

[4]

[Anonymous], 1978, Stud. Math. Appl.

[5] A SOBOLEV INEQUALITY AND THE INDIVIDUAL INVARIANCE PRINCIPLE FOR DIFFUSIONS IN A PERIODIC POTENTIAL [J].

Ba, Moustapha ;

Mathieu, Pierre .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (03) :2022-2043

[6]

Bailescu L., 2019, Z ANGEW MATH PHYS, V70

[7] Recent progress on the Random Conductance Model [J].

Biskup, Marek .

PROBABILITY SURVEYS, 2011, 8 :294-373

[8]

Chen X., ARXIV200308581

[9]

Chen X., ANN APPL PROBAB

[10] Random conductance models with stable-like jumps: Heat kernel estimates and Harnack inequalities [J].

Chen, Xin ;

Kumagai, Takashi ;

Wang, Jian .

JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (07)

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