L\'evy-type processes: convergence and discrete schemes
Probability
2017-09-12 v2
Abstract
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes in order to obtain convergence results on discrete and continuous time indexed processes, simulation methods and Euler schemes. We also apply the same theory to a slightly different situation, in order to get results of convergence of diffusions or random walks toward singular diffusions. As a consequence we deduce the convergence of random walks in random medium toward diffusions in random potential.
Cite
@article{arxiv.1707.02889,
title = {L\'evy-type processes: convergence and discrete schemes},
author = {Mihai Gradinaru and Tristan Haugomat},
journal= {arXiv preprint arXiv:1707.02889},
year = {2017}
}