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

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  • Xi, Fubao
  • Zhu, Chao

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.

Suggested Citation

  • Xi, Fubao & Zhu, Chao, 2018. "On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4277-4308.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:12:p:4277-4308
    DOI: 10.1016/j.spa.2018.02.005
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    References listed on IDEAS

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    1. Xi, Fubao, 2009. "Asymptotic properties of jump-diffusion processes with state-dependent switching," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2198-2221, July.
    2. Feng, S. & Zheng, X., 1992. "Solutions of a class of nonlinear master equations," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 65-84, November.
    3. Wang, Jian, 2010. "Regularity of semigroups generated by Lévy type operators via coupling," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1680-1700, August.
    4. Bass, Richard F. & Tang, Huili, 2009. "The martingale problem for a class of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1144-1167, April.
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