Volume 10, September 2006
|Page(s)||380 - 405|
|Published online||20 October 2006|
SPDEs with coloured noise: Analytic and stochastic approaches
Dipartimento di Matematica,
Università di Padova, Via Belzoni 7, 35131 Padova, Italy;
2 Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; email@example.com
Revised: 29 March 2006
We study strictly parabolic stochastic partial differential equations on , 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.
Mathematics Subject Classification: 60H15 / 60H25 / 35R60
Key words: Stochastic partial differential equations / mild and weak solutions / random noise.
© EDP Sciences, SMAI, 2006
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