Laplace transform identities and measure-preserving transformations on the Lie-Wiener-Poisson spaces. (English) Zbl 1262.60051
In an abstract setting, which can be applied to the Wiener space, the path space over a Lie group, and the Poisson space, consider the divergence operator \(\delta\) (or the Skorohod integral). Various formulae are proved for the derivative of the Laplace transform \(\lambda\mapsto \operatorname{E}[e^{\lambda\delta(u)}]\). These expressions are used for measure characterisation and to prove the invariance of some transformations.
Reviewer: Jean Picard (Aubière)
MSC:
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
Keywords:
Malliavin calculus; Skorohod integral; measure invariance; covariant derivatives; quasi-nilpotence; path space; Lie groups; Poisson spaceReferences:
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