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

Abstract: In this short note we study homogenization of symmetric $d$-dimensional L\'evy 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 L\'evy processes on $\mathbb{R}^d$ and we identify -- using Mosco convergence -- the limit process.