1. Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces
- Author
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Privault, Nicolas
- Subjects
- *
LAPLACE transformation , *MEASURE theory , *POISSON algebras , *DIVERGENCE theorem , *OPERATOR theory , *PROBABILITY theory , *LIE groups , *GAUSSIAN distribution - Abstract
Abstract: Given a divergence operator δ on a probability space such that the law of is infinitely divisible with characteristic exponent we derive a family of Laplace transform identities for the derivative when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Carleman–Fredholm determinant of a covariant derivative operator and the characteristic exponent (0.1), in a general framework that includes the Wiener space, the path space over a Lie group, and the Poisson space. We use these expressions for measure characterization and to prove the invariance of transformations having a quasi-nilpotent covariant derivative, for Gaussian and other infinitely divisible distributions. [Copyright &y& Elsevier]
- Published
- 2012
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