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Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces
- Source :
-
Journal of Functional Analysis . Nov2012, Vol. 263 Issue 10, p2993-3023. 31p. - Publication Year :
- 2012
-
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]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 263
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 82111742
- Full Text :
- https://doi.org/10.1016/j.jfa.2012.07.017