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

  • Joris Bierkens
  • Onno van Gaans
  • Sjoerd Verduyn Lunel
Open Access
Article

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.

Mathematics Subject Classification (2000)

Primary 60H10 Secondary 47D06 

Keywords

Delay equation Eventually compact semigroup Invariant measure Reaction diffusion equation Stochastic evolution equation Tightness 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Joris Bierkens
    • 1
  • Onno van Gaans
    • 1
  • Sjoerd Verduyn Lunel
    • 1
  1. 1.Mathematical InstituteLeidenThe Netherlands

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