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Title: On a unique ergodicity of some Markov processes
Authors: Kapica, Rafał
Szarek, Tomasz
Ślęczka, Maciej
Keywords: Ergodicity of Markov families; Invariant measures; Stochastic heat equations
Issue Date: 2012
Citation: Potential Analysis, Vol. 36 (2012), s. 589-606
Abstract: 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 timehomogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given.
DOI: 10.1007/s11118-011-9242-0
ISSN: 0926-2601
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