A ug 2 00 4 SPDEs with coloured noise : Analytic and stochastic approaches
نویسندگان
چکیده
We study strictly parabolic stochastic partial differential equations on 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.
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تاریخ انتشار 2004