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 (Unpublished)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