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

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H15 Stochastic partial differential equations, See also {35R60}
- 60G15 Gaussian processes
- 35G10 Initial value problems for linear higher-order PDE, linear evolution equations
- 60G17 Sample path properties

**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