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Spatial regularity of semigroups generated by Lévy type operators
Author(s) -
Liang Mingjie,
Wang Jian
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800181
Subject(s) - mathematics , lipschitz continuity , type (biology) , semigroup , martingale (probability theory) , pure mathematics , probabilistic logic , mathematical analysis , statistics , ecology , biology
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.