Girsanov identities for Poisson measures under quasi-nilpotent transformations
Nicolas Privault
Source: Ann. Probab. Volume 40, Number 3
(2012), 1009-1040.
Abstract
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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Keywords: Poisson measures; random transformations; Girsanov identities; quasi-invariance; invariance; Skorohod integral; moment identities; Stirling numbers
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1336136057
Digital Object Identifier: doi:10.1214/10-AOP640
Zentralblatt MATH identifier: 06047798
Mathematical Reviews number (MathSciNet): MR2962085
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