Abstract
This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes (X(t),Λ(t)), where Λ(t) is a component representing discrete events taking values in a countably infinite set. Considering the corresponding stochastic differential equations, our main focus is on treating those with non-Lipschitz coefficients. We first show that there exists a unique strong solution to the corresponding stochastic differential equation. Then Feller and strong Feller properties are investigated.
The study was initiated during a workshop held at IMA, University of Minnesota. The support of IMA with funding provided by the National Science Foundation is acknowledged. The research was also supported in part by the National Natural Science Foundation of China under Grant No. 11671034, the US Army Research Office, and the Simons Foundation Collaboration Grant (No. 523736).
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Xi, F., Yin, G., Zhu, C. (2019). Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties. In: Yin, G., Zhang, Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-030-25498-8_23
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