Girsanov identities for Poisson measures under quasi-nilpotent transformations.
Date of Issue2012
School of Physical and Mathematical Sciences
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.
The annals of probability
© 2012 Institute of Mathematical Statistics. This paper was published in The Annals of Probability and is made available as an electronic reprint (preprint) with permission of Institute of Mathematical Statistics. The paper can be found at the following official DOI: [http://dx.doi.org/10.1214/10-AOP640]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.