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January, 1995 Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces
Szymon Peszat, Jerzy Zabczyk
Ann. Probab. 23(1): 157-172 (January, 1995). DOI: 10.1214/aop/1176988381

Abstract

It is shown that the transition semigroup $(P_t)_{t\geq0}$ corresponding to a nonlinear stochastic evolution equation is strong Feller and irreducible, provided the nonlinearities are Lipschitz continuous and the diffusion term is nondegenerate. This result ensures the uniqueness of the invariant measure for $(P_t)_{t\geq0}$.

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Szymon Peszat. Jerzy Zabczyk. "Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces." Ann. Probab. 23 (1) 157 - 172, January, 1995. https://doi.org/10.1214/aop/1176988381

Information

Published: January, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0831.60083
MathSciNet: MR1330765
Digital Object Identifier: 10.1214/aop/1176988381

Subjects:
Primary: 60J35
Secondary: 60H15, 60J25

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 1 • January, 1995
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