English

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.

Keywords

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

R2 v1 2026-06-23T01:19:59.550Z