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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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
Keywords
- Stochastic Process
- Perturbation Theory
- Probability Theory
- Invariant Measure
- Mathematical Biology