Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with Lévy Noise

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 Lévy 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 Lévy process.

References in corpus (4)

• On the Poisson equation and diffusion approximation 3
• Heat kernel estimates for non-symmetric stable-like processes
• Multiscale Finite Element methods for advection-dominated problems in perforated domains
• Fluctuations in the Homogenization of Semilinear Equations with Random Potentials

Cited by in corpus (1)

• Periodic Homogenization of a Lévy-Type Process with Small Jumps