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August 2022 Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise
Qiao Huang, Jinqiao Duan, Renming Song
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Bernoulli 28(3): 1648-1674 (August 2022). DOI: 10.3150/21-BEJ1365

Abstract

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 α-stable Lévy noise (1<α<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 α-stable Lévy process.

Acknowledgements

We would like to thank the reviewers for their thoughtful comments and efforts towards improving our manuscript. The research of J. Duan was partly supported by the NSF grant 1620449. The research of Q. Huang was partly supported by China Scholarship Council (CSC), and NSFC grants 11531006 and 11771449. The research of R. Song is supported in part by a grant from the Simons Foundation (# 429343, Renming Song).

Citation

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Qiao Huang. Jinqiao Duan. Renming Song. "Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise." Bernoulli 28 (3) 1648 - 1674, August 2022. https://doi.org/10.3150/21-BEJ1365

Information

Received: 1 October 2019; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1365

Keywords: Feller semigroups , Feynman-Kac formula , Homogenization‎ , nonlocal parabolic PDEs , SDEs with jumps , strong well-posedness , Zvonkin’s transform

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Vol.28 • No. 3 • August 2022
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