We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions.
Jinying Tong. "Feller Property for a Special Hybrid Jump-Diffusion Model." Abstr. Appl. Anal. 2014 (SI35) 1 - 8, 2014. https://doi.org/10.1155/2014/412848