Probability Theory
Moment identities for Poisson–Skorohod integrals and application to measure invariance
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1071-1074.

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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DOI: 10.1016/j.crma.2009.07.010
Privault, Nicolas 1

1 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
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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] Dermoune, A.; Krée, P.; Wu, L. 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] Nualart, D.; Vives, J. 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] Di Nunno, G.; Øksendal, B.; Proske, F. Malliavin Calculus for Lévy Processes with Applications to Finance, Universitext, Springer-Verlag, Berlin, 2009

[4] Picard, J. 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] Privault, N. Moment identities for Skorohod integrals on the Wiener space applications, Electron. Commun. Probab., Volume 14 (2009), pp. 116-121 (electronic)

[7] Privault, N. Stochastic Analysis in Discrete and Continuous Settings, Lecture Notes in Mathematics, vol. 1982, Springer-Verlag, Berlin, 2009

[8] Üstünel, A.S.; Zakai, M. 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).