Periodic measures for a class of SPDEs with regime-switching

TL;DR

This paper investigates the existence and uniqueness of periodic measures for a class of stochastic partial differential equations with regime-switching driven by degenerate Lévy noise, using variational and Lyapunov methods.

Contribution

It introduces a novel approach combining variational and Lyapunov methods to establish periodic measures for SPDEs with regime-switching and degenerate Lévy noise.

Findings

Established existence of periodic measures.

Proved uniqueness of periodic measures.

Applied results to stochastic porous media equations.

Abstract

We use the variational approach to investigate periodic measures for a class of SPDEs with regime-switching. The hybrid system is driven by degenerate L\'{e}vy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the associated time-inhomogeneous semigroup. The main results are applied to stochastic porous media equations with regime-switching.