Document ESAIM: P&S, October 2006, Vol. 10, pp. 380-405
DOI: 10.1051/ps:2006016
SPDEs with coloured noise: Analytic and stochastic approaches
Marco Ferrante1 and Marta Sanz-Solé21 Dipartimento di Matematica, Università di Padova, Via Belzoni 7, 35131 Padova, Italy; ferrante@math.unipd.it
2 Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; marta.sanz@ub.edu
(Received February 22, 2005. Revised March 29, 2006. Published online 20 October 2006.)
Abstract
We study strictly
parabolic stochastic partial differential equations on
, 
,
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