Summary
We prove the existence of an invariant measure for processes arising from a perturbation of theC[0,1]-valued Ornstein-Uhlenbeck process with a drift taking values in the Cameron-Martin space. We study the infinitesimal generator, and a partial integration onC[0,1] will yield conditions on the drift which enable us to use arguments of perturbation theory to prove the existence of an invariant measure which is absolutely continuous with respect to the Wiener measure.
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References
Gross, L.: Abstract Wiener spaces. Proc. 5th Berkeley Symp. Math. Stat. Probab.2, (1965)
Kato, T.: Perturbation theory for linear operators (2nd edition). Berlin Heidelberg New York: Springer 1976
Ocone, D.: Malliavin's calculus and stochastic integral representation of functionals of diffusion processes. Stochastics12, (1984)
Shigekawa, I.: Existence of invariant measures of diffusions on an abstract Wiener space. Osaka J. Math.24, (1987)
Shigekawa, I.: Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ.20, (1980)
Sugita, H.: Sobolev spaces of Wiener functionals and Malliavin's calculus. J. Math. Kyoto Univ.25, (1985)
Vintschger, R.v.: Zeitumkehr und invariante Masse für Diffusionen auf einem Wienerraum. Diss. ETH 8356, 1987
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Vintschger, R.v. The existence of invariant measures forC[0,1]-valued diffusions. Probab. Th. Rel. Fields 82, 307–313 (1989). https://doi.org/10.1007/BF00354766
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DOI: https://doi.org/10.1007/BF00354766