Local Coupling Property for Markov Processes with Applications to L\'evy Processes
Probability
2018-02-28 v1
Abstract
In this article, we define the new concept of local coupling property for Markov processes and study its relationship with distributional properties of the transition probability. In the special case of L\'evy processes we show that this property is equivalent to the absolute continuity of the transition probability and also provide a sufficient condition for it in terms of the L\'evy measure. Our result is stronger than existing results for absolute continuity of L\'evy distributions.
Keywords
Cite
@article{arxiv.1802.09608,
title = {Local Coupling Property for Markov Processes with Applications to L\'evy Processes},
author = {Kasra Alishahi and Erfan Salavati},
journal= {arXiv preprint arXiv:1802.09608},
year = {2018}
}