We present a moment identity on the Poisson space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral. Applications of this identity are given to the invariance of Poisson measures under intensity preserving random transformations.
Nous présentons une identité de moments sur l'espace de Poisson qui étend l'isométrie de Skorohod à des puissances quelconques de l'intégrale de Skorohod, et nous étudions les applications de cette identité à l'invariance de la mesure de Poisson sous les tranformations aléatoires qui préservent l'intensité.
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Nicolas Privault 1
@article{CRMATH_2009__347_17-18_1071_0, author = {Nicolas Privault}, title = {Moment identities for {Poisson{\textendash}Skorohod} integrals and application to measure invariance}, journal = {Comptes Rendus. Math\'ematique}, pages = {1071--1074}, publisher = {Elsevier}, volume = {347}, number = {17-18}, year = {2009}, doi = {10.1016/j.crma.2009.07.010}, language = {en}, }
TY - JOUR AU - Nicolas Privault TI - Moment identities for Poisson–Skorohod integrals and application to measure invariance JO - Comptes Rendus. Mathématique PY - 2009 SP - 1071 EP - 1074 VL - 347 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2009.07.010 LA - en ID - CRMATH_2009__347_17-18_1071_0 ER -
Nicolas Privault. Moment identities for Poisson–Skorohod integrals and application to measure invariance. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1071-1074. doi : 10.1016/j.crma.2009.07.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.010/
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☆ The work described in this paper was substantially supported by a grant from City University of Hong Kong (Project No. 7002312).
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