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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@article{CRMATH_2009__347_17-18_1071_0, author = {Privault, Nicolas}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.07.010/} }
TY - JOUR AU - Privault, Nicolas 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2009.07.010/ DO - 10.1016/j.crma.2009.07.010 LA - en ID - CRMATH_2009__347_17-18_1071_0 ER -
%0 Journal Article %A Privault, Nicolas %T Moment identities for Poisson–Skorohod integrals and application to measure invariance %J Comptes Rendus. Mathématique %D 2009 %P 1071-1074 %V 347 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.07.010/ %R 10.1016/j.crma.2009.07.010 %G en %F CRMATH_2009__347_17-18_1071_0
Privault, Nicolas. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.07.010/
[1] Calcul stochastique non adapté par rapport à la mesure de Poisson, Séminaire de Probabilités XXII (Lecture Notes in Mathematics), Volume vol. 1321, Springer Verlag (1988), pp. 477-484
[2] A duality formula on the Poisson space some applications, Ascona, 1993 (Dalang, R.; Dozzi, M.; Russo, F., eds.) (Progress in Probability), Volume vol. 36, Birkhäuser, Basel (1995), pp. 205-213
[3] Malliavin Calculus for Lévy Processes with Applications to Finance, Universitext, Springer-Verlag, Berlin, 2009
[4] Formules de dualité sur l'espace de Poisson, Ann. Inst. H. Poincaré Probab. Statist., Volume 32 (1996) no. 4, pp. 509-548
[5] N. Privault, Invariance of Poisson measures under random transformations, preprint, 2009
[6] Moment identities for Skorohod integrals on the Wiener space applications, Electron. Commun. Probab., Volume 14 (2009), pp. 116-121 (electronic)
[7] Stochastic Analysis in Discrete and Continuous Settings, Lecture Notes in Mathematics, vol. 1982, Springer-Verlag, Berlin, 2009
[8] Random rotations of the Wiener path, Probab. Theory Relat. Fields, Volume 103 (1995) no. 3, pp. 409-429
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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).