Regularity of semigroups generated by Lévy type operators via coupling |
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Authors: | Jian Wang |
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Affiliation: | School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, PR China; Institut für Mathematische Stochastik, TU Dresden, Dresden, 01062, Germany |
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Abstract: | By adopting the coupling method, we obtain new verifiable sufficient conditions about the Cb(Rd)-Feller continuity, the Lipschitz continuity and the strong Feller continuity of the semigroups associated with Lévy type operators. These results easily apply to jump–diffusion processes and stochastic differential equations driven by Lévy processes. Our results also yield the criterion for the e-property (namely the characterization about the equi-continuity of semigroups acting on bounded Lipschitz functions) of Lévy type operators, and show that both genuine Lévy processes and the Ornstein–Uhlenbeck type processes are e-processes. |
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Keywords: | 60J25 60J75 60J35 |
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