Recurrence and periodicity for stochastic differential equations with regime-switching jump diffusions
Yue Gao, Xiaomeng Jiang, Yong Li · Discrete and Continuous Dynamical Systems - B · 2023
In this paper, we consider a regime-switching jump diffusion process (RSJDP) generated by a nonautonomous stochastic differential equation. First, we show that the underlying process is recurrent, positive recurrent and transient in a finite state space or an infinite countable state space. Then we prove the existence of periodic solutions in distribution. Finally, we give some examples to illustrate our criteria.