On a Unique Ergodicity of Some Markov Processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to time-homogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given.

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