Spatial regularity of semigroups generated by L\'{e}vy type operators
Probability
2018-04-12 v1
Abstract
We apply the probabilistic coupling approach to establish the spatial regularity of semigroups associated with L\'{e}vy type operators, by assuming that the martingale problem of L\'{e}vy type operators is well posed. In particular, we can prove the Lipschitz continuity of the semigroups under H\"{o}lder continuity of coefficients, even when the L\'evy kernel corresponding to L\'{e}vy type operators is singular.
Cite
@article{arxiv.1804.03781,
title = {Spatial regularity of semigroups generated by L\'{e}vy type operators},
author = {Mingjie Liang and Jian Wang},
journal= {arXiv preprint arXiv:1804.03781},
year = {2018}
}
Comments
18 pages