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On asymptotic stability and sweeping for Markov operators. (English) Zbl 0838.47040
Summary: New conditions for asymptotic stability and sweeping of Markov operators are given. These criteria are applied to semigroups of Markov operators generated by partial differential equations.

47G10 Integral operators
47B38 Linear operators on function spaces (general)
47D07 Markov semigroups and applications to diffusion processes
47A35 Ergodic theory of linear operators
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