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Invariant measures for generalized Langevin equations in conuclear space

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  • Bojdecki, Tomasz
  • Jakubowski, Jacek

Abstract

We investigate existence of an invariant probability measure for the equation in a conuclear space [Phi]', where W is a Wiener process in [Phi]' and generates a semigroup in [Phi]. In the first part of the paper we formulate a sufficient and necessary condition for the existence of an invariant measure and we describe all invariant measures. In the second part we investigate the case and (the fractional Laplacian) for 0

Suggested Citation

  • Bojdecki, Tomasz & Jakubowski, Jacek, 1999. "Invariant measures for generalized Langevin equations in conuclear space," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 1-24, November.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:1-24
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    References listed on IDEAS

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    1. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    2. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
    3. Dawson, Donald A. & Salehi, Habib, 1980. "Spatially homogeneous random evolutions," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 141-180, June.
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    1. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
    2. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.

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