Laplace transform identities and measure-preserving transformations on the Lie–Wiener–Poisson spaces

• Main Author: Privault, Nicolas
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Mathematics::Analysis
• Online Access: https://hdl.handle.net/10356/97911; http://hdl.handle.net/10220/17123
• Institution: Nanyang Technological University

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.