Regularity of semigroups generated by Lévy type operators via coupling

Jian Wang

Stochastic Processes and their Applications, 2010, vol. 120, issue 9, 1680-1700

Abstract: 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.

Keywords: Lévy; type; operators; -Feller; continuity; Lipschitz; continuity; Strong; Feller; continuity; Coupling; Feller; processes; e-property (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (7)

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