Preprint series: 07-10 , Reports on Analysis

MSC:

60H20 Stochastic integral equations

60H05 Stochastic integrals

26A33 Fractional derivatives and integrals

60G15 Gaussian processes

60G18 Self-similar processes

60G10 Stationary processes

Abstract: Aim of this work is to extend the results of
Clément, Da Prato & Prüss on the fractional white noise
perturbation with Hurst parameter $H\in(0,1)$. We will obtain
similar results and it will turn out that the regularity of the
solution $u(t)$ increases with Hurst parameter
$H$.

Keywords: fractional Brownian motion, fractional integration, fractional derivatives, Volterra equations, stochastic convolution, parabolicity, linear viscoelasticity

Upload: 2007-04-17