Homogenization of Symmetric Lévy Processes on ${\mathbb{R}}^d$

Abstract

In this short note we study homogenization of symmetric $d$-dimensional Lévy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \emph{et al.} in 1992; their motivation was the work by Benssousan \emph{et al.}\ from 1975 on the homogenization of diffusion processes in ${\mathbb{R}}^d$. We investigate a similar problem for a class of symmetric pure-jump Lévy processes on ${\mathbb{R}}^d$ and we identify -- using Mosco convergence -- the limit process.

Cited by in corpus (1)

• Homogenization of symmetric stable-like processes in stationary ergodic medium