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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Xi, Fubao¹  Zhu, Chao² 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

关键词: Weakly coupled Levy type operator;    Martingale problem;    Feller property;    Strong Feller property;    Coupling method;   

DOI  :  10.1016/j.spa.2018.02.005

来源: Elsevier

【 摘 要 】

This paper considers the martingale problem for a class of weakly coupled Levy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process (X, Lambda). The process (X, Lambda), called a regime-switching jump diffusion with Levy type jumps, is further shown to possess Feller and strong Feller properties under non-Lipschitz conditions via the coupling method. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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