Homogenization of nonlocal partial differential equations related to stochastic differential equations with Levy noise

被引：3

作者：

Huang, Qiao ^{[1
]}

Duan, Jinqiao ^{[2
]}

Song, Renming ^{[3
]}

机构：

[1] Huazhong Univ Sci & Technol, Ctr Math Sci, Wuhan 430074, Hubei, Peoples R China

[2] Illinois Inst Technol, Dept Appl Math, Chicago, IL 60616 USA

[3] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

来源：

BERNOULLI | 2022年 / 28卷 / 03期

关键词：

Homogenization; nonlocal parabolic PDEs; SDEs with jumps; Zvonkin's transform; strong well-posedness; Feller semigroups; Feynman-Kac formula; PERIODIC HOMOGENIZATION; SDES DRIVEN; DIFFUSION; COEFFICIENTS; OPERATORS;

D O I：

10.3150/21-BEJ1365

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the "periodic homogenization" for a class of nonlocal partial differential equations of parabolic-type with rapidly oscillating coefficients, related to stochastic differential equations driven by multiplicative isotropic alpha-stable Levy noise (1 < alpha < 2) which is nonlinear in the noise component. Our homogenization method is probabilistic. It turns out that, under suitable regularity assumptions, the limit of the solutions satisfies a nonlocal partial differential equation with constant coefficients, which are associated to a symmetric alpha-stable Levy process.

引用

页码：1648 / 1674

页数：27

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