Université Paul Sabatier Toulouse

CNRS U.M.R. C5583
Laboratoire de Statistique et Probabilités

Stochastic analysis, rough path analysis and fractional Brownian motions.

L. Coutin, Z.Qian

Code(s) de Classification MSC:

Résumé: Inthis paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of this geometric rough path. By the results in [?], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordlingly. The method can actually be applied to a larger class of Gaussian processes with covariance functions satisfying a simple decay conditions.

Mots Clés: fractional Brownian motion, Gaussian process, Malliavin calculus, rough path, stochastic differential equation.

Date: 2000-07-03

Prépublication numéro: LSP-2000-13