Probability Theory
Cumulant operators and moments of the Itô and Skorohod integrals
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 397-400.

We propose a formula for the computation of the moments of all orders of Itô and Skorohod stochastic integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. Some characterizations of Gaussian distributions for stochastic integrals are recovered as a consequence.

Nous proposons une formule de calcul des moments dʼintégrales dʼItô et de Skorohod par rapport au mouvement brownien à lʼaide dʼopérateurs cumulants définis par le calcul de Malliavin. On retrouve ainsi certaines caractérisations de la loi gaussienne pour les intégrales stochastiques.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.05.014
Privault, Nicolas 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore
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Privault, Nicolas. Cumulant operators and moments of the Itô and Skorohod integrals. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 397-400. doi : 10.1016/j.crma.2013.05.014. http://www.numdam.org/articles/10.1016/j.crma.2013.05.014/

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