On Parabolic Volterra Equations Disturbed by Fractional Brownian Motions
نویسنده
چکیده
Aim of this paper is to study the parabolic Volterra equation u(t) + (b ∗Au)(t) = (QB)(t), t ≥ 0, on a separable Hilbert space. Throughout this work the operator −A is assumed to be a differential operator like the Laplacian, the elasticity operator, or the Stokes operator. The random disturbance Q1/2BH is modeled to be a system independent vector valued fractional Brownian motion with Hurst parameter H ∈ (0, 1). We derive optimal conditions for the existence of a unique mild solution and the Hölderianity of its trajectories. For this purpose we do the analysis on stochastic integrals of the form ∫ ∞ 0 R(t)d(QB)(t), t ≥ 0, where the integrand R is a deterministic, operator valued function.
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تاریخ انتشار 2007