• S. TINDEL
• C.A. TUDOR
• F. VIENS

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