Summary
In this paper we consider the transformation of measure induced by a not-necessarily-invertible perturbation of the identity. The Radon-Nikodym density for the image of the Wiener measure and the associated Girsanov-type density are derived. An application of these results yields an extension of the degree theorem.
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Üstünel, A.S., Zakai, M. Transformation of the Wiener measure under non-invertible shifts. Probab. Th. Rel. Fields 99, 485–500 (1994). https://doi.org/10.1007/BF01206229
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DOI: https://doi.org/10.1007/BF01206229
Mathematics Subject Classification
- 60G30
- 60H07
- 60H010