Homogenization of Periodic Linear Nonlocal Partial Differential Equations
Qiao Huang, Jinqiao Duan, Renming Song · arXiv (Cornell University) · 2018
We study the periodic for a class of linear nonlocal partial differential equations of parabolic-type with rapidly oscillating coefficients, associated to stochastic differential equations driven by multiplicative isotropic $\alpha$-stable L\'evy noise for $1<\alpha<2$. Our homogenization method is probabilistic. It turns out that, under some weak regularity assumptions, the limit of the solutions satisfies a nonlocal partial differential equation with constant coefficients, associated to a symmetric $\alpha$-stable L\'evy process.