Summary
We study the absolute continuity of the image measure of the canonical Poisson probability measure under nonlinear shifts. The Radon-Nykodim density function is expressed using a Carleman-Fredholm determinant and a divergence operator. Results are obtained for non-necessarily invertible transformations, under almost-sure differentiability hypothesis.
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Privault, N. Girsanov theorem for anticipative shifts on Poisson space. Probab. Th. Rel. Fields 104, 61–76 (1996). https://doi.org/10.1007/BF01303803
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DOI: https://doi.org/10.1007/BF01303803
Mathematics Subject Classification
- 60G30
- 60G55
- 60H07