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arXiv · 1804.03781

Spatial regularity of semigroups generated by L\'{e}vy type operators

Mingjie Liang·Jian Wang
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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.

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Mingjie Liang, Jian Wang. 2018-04-11. Spatial regularity of semigroups generated by L\'{e}vy type operators. https://arxiv.org/abs/1804.03781

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