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SPDEs with coloured noise: Analytic and stochastic approaches

Published online by Cambridge University Press:  20 October 2006

Marco Ferrante
Affiliation:
Dipartimento di Matematica, Università di Padova, Via Belzoni 7, 35131 Padova, Italy; ferrante@math.unipd.it
Marta Sanz-Solé
Affiliation:
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; marta.sanz@ub.edu
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Abstract

We study strictly parabolic stochastic partial differential equations on $\mathbb{R}^d$, d ≥ 1, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give sufficient conditions on the correlation of the noise ensuring Hölder continuity for the trajectories of the solution of the equation. For self-adjoint operators with deterministic coefficients, the mild and weak formulation of the equation are related, deriving path properties of the solution to a parabolic Cauchy problem in evolution form.


Type
Research Article
Copyright
© EDP Sciences, SMAI, 2006

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