Geodesic
SPDEs with coloured noise : analytic and stochastic approaches
ESAIM: Probability and Statistics, Tome 10 (2006), pp. 380-405

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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.

DOI : 10.1051/ps:2006016
Classification : 60H15, 60H25, 35R60
Keywords: stochastic partial differential equations, mild and weak solutions, random noise 
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     author = {Ferrante, Marco and Sanz-Sol\'e, Marta},
     title = {SPDEs with coloured noise : analytic and stochastic approaches},
     journal = {ESAIM: Probability and Statistics},
     pages = {380--405},
     publisher = {EDP-Sciences},
     volume = {10},
     year = {2006},
     doi = {10.1051/ps:2006016},
     mrnumber = {2263072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2006016/}
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Ferrante, Marco; Sanz-Solé, Marta. SPDEs with coloured noise : analytic and stochastic approaches. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 380-405. doi: 10.1051/ps:2006016

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