On a unique ergodicity of some Markov processes
The authors prove that any weakly irreducible e-process admits at most one invariant measure. The stochastic process on \(X\) given by a semigroup \((P_t)_{t\geq0}\) is called e-process if it satisfies the e-property: for any point \(x\in X\) and an arbitrary Lipschitz bounded function \(\phi: X\to \mathbb{R}\) the family \(\{P_t\phi(x)\}_{t\geq0}\) is equicontinuous in \(x\). Some application to time-homogeneous Markov process associated with a nonlinear heat equation driven by an impulsive noise is also given.
scientific article; zbMATH DE number 6031715
scientific article