Stochastic Integration with respect to Volterra processes

Laurent Decreusefond (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which are natural generalization of fractional Brownian motion, we construct a stochastic integral and show some of its main properties: regularity with respect to time and kernel, transformation under an absolutely continuous change of probability, possible approximation schemes and Itô formula.

Mots clés: Fractional Brownian motion; Malliavin calculus; stochastic integral

Domaines: Probabilités [math.PR]

Laurent Decreusefond. Stochastic Integration with respect to Volterra processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2005, 41, pp.123-149. ⟨hal-00358143⟩