Volterra equations perturbed by noise

Bonaccorsi, Stefano and Desch, Wolfgang (2006) Volterra equations perturbed by noise. UNSPECIFIED. (Unpublished)

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    Abstract

    We consider a linear abstract Volterra integrodifferential equation in a Hilbert space, forced by a Gaussian process. The equation involves a completely monotone convolution kernel with a singularity at t = 0 and a sectorial linear spatial operator. Existence and uniqueness of a weak solution is established. Furthermore we give conditions such that the solution converges to a stationary process. Our method consists in a state space setting so that the corresponding solution process is Markovian, and the tools of linear analytic semigroup theory can be utilized.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA374.7 Partial differential equations
    Uncontrolled Keywords: Abstract integrodifferential equation, stochastic forcing, singular kernel, stationary state, analytic semigroup. MSC 2000: 60H15, 60H20, 45K05.
    Report Number: UTM 698, June 2006
    Repository staff approval on: 03 Jul 2006

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