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Ergodicity

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1762)

Abstract

In the chapters 4, 6 and 7 we have proved that the semigroup Pt corresponding to the system du(t) = [Au(t)+F(u(t))]dt + Qdw(t), u(0) = x, (8.0.1) has a regularizing effect both in E and in H. Here we apply these results to the proof of the existence of a unique invariant measure μ, for the semigroup P t, which is equivalent to all transition probabilities P t(x,.), t > 0 and xH, and which is concentrated on the space of continuous functions E.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Ergodicity. In: Cerrai, S. (eds) Second Order PDE’s in Finite and Infinite Dimension. Lecture Notes in Mathematics, vol 1762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45147-1_9

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  • DOI: https://doi.org/10.1007/3-540-45147-1_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42136-8

  • Online ISBN: 978-3-540-45147-1

  • eBook Packages: Springer Book Archive