Open Access
Translator Disclaimer
May 2012 Girsanov identities for Poisson measures under quasi-nilpotent transformations
Nicolas Privault
Ann. Probab. 40(3): 1009-1040 (May 2012). DOI: 10.1214/10-AOP640

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.

Citation

Download Citation

Nicolas Privault. "Girsanov identities for Poisson measures under quasi-nilpotent transformations." Ann. Probab. 40 (3) 1009 - 1040, May 2012. https://doi.org/10.1214/10-AOP640

Information

Published: May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1248.60056
MathSciNet: MR2962085
Digital Object Identifier: 10.1214/10-AOP640

Subjects:
Primary: 11B73 , 28C20 , 28D05 , 60G30 , 60G57 , 60H07

Keywords: Girsanov identities , Invariance , Moment identities , Poisson measures , Quasi-invariance , Random transformations , Skorohod integral , Stirling numbers

Rights: Copyright © 2012 Institute of Mathematical Statistics

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.40 • No. 3 • May 2012
Back to Top