Periodic measures for a class of SPDEs with regime-switching
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\'evy 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.
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