Existence of an invariant measure for stochastic evolutions driven by an eventually compact semigroup

J. Bierkens; O.W. van Gaans; Sjoerd Verduyn Lunel

Existence of an invariant measure for stochastic evolutions driven by an eventually compact semigroup

J. Bierkens, O.W. van Gaans, Sjoerd Verduyn Lunel

Sub Mathematical Modeling

Leiden University

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

Original language	English
Article number	1424-3199/09/040771-16
Pages (from-to)	771-786
Journal	Journal of Evolution Equations
Volume	9
Publication status	Published - 2009

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title = "Existence of an invariant measure for stochastic evolutions driven by an eventually compact semigroup",

abstract = "It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.",

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year = "2009",

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AU - Bierkens, J.

AU - van Gaans, O.W.

AU - Verduyn Lunel, Sjoerd

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Y1 - 2009

N2 - It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

AB - It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

M3 - Article

SN - 1424-3202

VL - 9

SP - 771

EP - 786

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

M1 - 1424-3199/09/040771-16

ER -

Existence of an invariant measure for stochastic evolutions driven by an eventually compact semigroup

Abstract

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