The Annals of Probability

Girsanov identities for Poisson measures under quasi-nilpotent transformations

Nicolas Privault

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We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals.

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Ann. Probab., Volume 40, Number 3 (2012), 1009-1040.

First available in Project Euclid: 4 May 2012

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Primary: 60G57: Random measures 60G30: Continuity and singularity of induced measures 60H07: Stochastic calculus of variations and the Malliavin calculus 28D05: Measure-preserving transformations 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 11B73: Bell and Stirling numbers

Poisson measures random transformations Girsanov identities quasi-invariance invariance Skorohod integral moment identities Stirling numbers


Privault, Nicolas. Girsanov identities for Poisson measures under quasi-nilpotent transformations. Ann. Probab. 40 (2012), no. 3, 1009--1040. doi:10.1214/10-AOP640.

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