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arXiv · 1804.06555

Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with L\'evy Noise

Qiao Huang·Jinqiao Duan·Renming Song
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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 $\alpha$-stable L\'evy 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 L\'evy process.

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Qiao Huang, Jinqiao Duan, Renming Song. 2018-04-18. Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with L\'evy Noise. https://arxiv.org/abs/1804.06555

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