Abstract
We consider a Banach space valued diffusion process corresponding to a stochastic evolution equation with strongly nonlinear drift. Sufficient conditions are given for the existence of a unique martingale solution and existence of an invariant measure. The resulting diffusion process is shown to be strongly Feller and irreducible. These properties yield uniqueness of invariant measure and ergodicity of the process. We also show that the invariant measure is equivalent to the invariant measure of the diffusion without drift. The main tool to show these results is the Girsanov Transformation.
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Gatarek, D., Goldys, B. On Invariant Measures for Diffusions on Banach Spaces. Potential Analysis 7, 533–553 (1997). https://doi.org/10.1023/A:1008663614438
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DOI: https://doi.org/10.1023/A:1008663614438