Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties

Fubao Xi; George Yin; Chao Zhu

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arXiv · 1810.08334

Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties

Fubao Xi·George Yin·Chao Zhu

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Abstract

This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),\Lambda(t))$, where $\Lambda(t)$ 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.

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Fubao Xi, George Yin, Chao Zhu. 2018-10-19. Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties. https://arxiv.org/abs/1810.08334

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