Periodic homogenization of discontinuous Markov processes
In this talk, I will present some recent results on
homogenization of discontinuous Markov processes with Levy type generators
in periodic media. Under a proper scaling, the scaled Markov process is
shown to converge weakly to a Levy process. Different phenomena occur
depending on the tails of the jumping kernel of the discontinuous Markov
process. These results can be viewed as the non-local counterparts of the
celebrated work of Bensoussan-Lions-Papanicoaou and Bhattacharya for
diffusions.