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Title: Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces
Authors: Privault, Nicolas
Keywords: DRNTU::Science::Mathematics::Analysis
Issue Date: 2012
Source: Privault, N. (2012). Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces. Journal of functional analysis, 263(10), 2993-3023.
Series/Report no.: Journal of functional analysis
Abstract: Given a divergence operator δ on a probability space such that the law of δ(h) is infinitely divisible with characteristic exponent we derive a family of Laplace transform identities for the derivative ∂E[eλδ(u)]/∂λ 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.
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.07.017
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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