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Spatial regularity of semigroups generated by Lévy type operators

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  • Mingjie Liang
  • Jian Wang

Abstract

We apply the probabilistic coupling approach to establish spatial regularity of semigroups associated with Lévy type operators, by assuming that the corresponding martingale problem is well posed. In particular, we can prove the Lipschitz continuity of the associated semigroups, when the coefficients are Hölder continuous but the corresponding Lévy kernel may be singular.

Suggested Citation

  • Mingjie Liang & Jian Wang, 2019. "Spatial regularity of semigroups generated by Lévy type operators," Mathematische Nachrichten, Wiley Blackwell, vol. 292(7), pages 1551-1566, July.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:7:p:1551-1566
    DOI: 10.1002/mana.201800181
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    Cited by:

    1. Franziska Kühn, 2021. "Schauder Estimates for Poisson Equations Associated with Non-local Feller Generators," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1506-1578, September.

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