Comptes Rendus
no. 17-18
Probability Theory
Moment identities for Poisson–Skorohod integrals and application to measure invariance
[Identités de moments pour les intégrales de Poisson–Skorohod et applications à l'invariance en mesure]

Présenté par : Paul Malliavin

Nicolas Privault1
1 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1071-1074.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.010
Nicolas Privault 1

1 Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong 
@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  - 
%0 Journal Article
%A Nicolas Privault
%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
%R 10.1016/j.crma.2009.07.010
%G en
%F CRMATH_2009__347_17-18_1071_0
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/

[1] A. Dermoune; P. Krée; L. Wu 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] D. Nualart; J. Vives A duality formula on the Poisson space some applications, Ascona, 1993 (R. Dalang; M. Dozzi; F. Russo, eds.) (Progress in Probability), Volume vol. 36, Birkhäuser, Basel (1995), pp. 205-213

[3] G. Di Nunno; B. Øksendal; F. Proske Malliavin Calculus for Lévy Processes with Applications to Finance, Universitext, Springer-Verlag, Berlin, 2009

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

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

[8] A.S. Üstünel; M. Zakai Random rotations of the Wiener path, Probab. Theory Relat. Fields, Volume 103 (1995) no. 3, pp. 409-429

Cité par Sources :

☆ The work described in this paper was substantially supported by a grant from City University of Hong Kong (Project No. 7002312).

Commentaires - Politique

Ces articles pourraient vous intéresser

Smoothness of Wigner densities on the affine algebra

Uwe Franz; Nicolas Privault; René Schott

C. R. Math (2003)

Cumulant operators and moments of the Itô and Skorohod integrals

Nicolas Privault

C. R. Math (2013)