Regularity of semigroups generated by Lévy type operators via coupling
By adopting the coupling method, we obtain new verifiable sufficient conditions about the -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.
Year of publication: |
2010
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Authors: | Wang, Jian |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 120.2010, 9, p. 1680-1700
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Publisher: |
Elsevier |
Keywords: | Lévy type operators -Feller continuity Lipschitz continuity Strong Feller continuity Coupling Feller processes e-property |
Saved in:
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