Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Stochastic evolution equations with fractional Brownian motion


Code(s) de Classification MSC:

Résumé: In this paper different types of stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. We consider first the case of the linear additive noise; a necessary and sufficient condition for the existence and uniqueness of the solution is established; separate proofs are required for the cases of Hurst parameter above and below 1/2. Moreover, we present a characterization of almost-sure moduli of continuity for the solution via a sharp theory of Gaussian regularity. Then we prove an existence and uniqueness result for the solution in the case of the linear equation with multiplicative noise and we derive a fractional stochastic Feynman-Kac formula.

Mots Clés: Fractional Brownian motion ; stochastic partial differential equation ; Feynman-Kac formula ; Gaussian regularity ; almost-sure modulus of continuity ; Hurst parameter.

Date: 2002-10-23

Prépublication numéro: PMA-764

Pdffile : PMA-764.pdf