On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators

Fubao Xi and Chao Zhu

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4277-4308

Abstract: This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process (X,Λ). The process (X,Λ), called a regime-switching jump diffusion with Lévy type jumps, is further shown to possess Feller and strong Feller properties under non-Lipschitz conditions via the coupling method.

Keywords: Weakly coupled Lévy type operator; Martingale problem; Feller property; Strong Feller property; Coupling method (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2018.02.005

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