Stationary distribution of periodic stochastic differential equations with Markov switching

Periodic stochastic differential equations (SDEs) with Markov switching are widely applied to describe various financial and biological phenomena in the real world and hence have been receiving intensive attention. One of the essential dynamical behaviours researchers are interested in is the asymptotic stability in distribution. However, related work on periodic SDEs is quite little. This paper aims to fill the gap. Technical challenges including time-inhomogeneity and periodicity of SDEs make this a challenging and non-trivial work. The main results are finally demonstrated by an example. Our theory can be easily implemented to different application scenarios.