Girsanov identities for Poisson measures under quasi-nilpotent transformations

• Autores: Nicolas Privault
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 3, 2012, págs. 1009-1040
• Idioma: inglés
• DOI: 10.1214/10-AOP640
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• Resumen

  • 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.