Wiener integrals, Malliavin calculus and covariance measure structure

Ida Kruk (1) , Francesco Russo (1) , Ciprian Tudor (2, 3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CES - Centre d'économie de la Sorbonne

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only when necessary. Our main examples are finite quadratric variation processes with stationary increments and the bifractional Brownian motion.

Mots clés: Square integrable processes; covariance measure structure; Malliavin calculus; Skorohod integral; bifractional Brownian motion.; bifractional Brownian motion

Domaines: Probabilités [math.PR]

Ida Kruk, Francesco Russo, Ciprian Tudor. Wiener integrals, Malliavin calculus and covariance measure structure. 2007. ⟨hal-00078163v2⟩