The Annals of Probability

Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces

Szymon Peszat and Jerzy Zabczyk

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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 $(P_t)_{t\geq0}$.

Article information

Source
Ann. Probab., Volume 23, Number 1 (1995), 157-172.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988381

Digital Object Identifier
doi:10.1214/aop/1176988381

Mathematical Reviews number (MathSciNet)
MR1330765

Zentralblatt MATH identifier
0831.60083

JSTOR
links.jstor.org

Subjects
Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 60J25: Continuous-time Markov processes on general state spaces

Keywords
Strong Feller property irreducible Markov semigroups invariant measures stochastic evolution equations

Citation

Peszat, Szymon; Zabczyk, Jerzy. Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces. Ann. Probab. 23 (1995), no. 1, 157--172. doi:10.1214/aop/1176988381. https://projecteuclid.org/euclid.aop/1176988381


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