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.
Classification : 60H15, 60H25, 35R60
Mots clés : stochastic partial differential equations, mild and weak solutions, random noise
@article{PS_2006__10__380_0,
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://www.numdam.org/articles/10.1051/ps:2006016/}
}
TY - JOUR AU - Ferrante, Marco AU - Sanz-Solé, Marta TI - SPDEs with coloured noise : analytic and stochastic approaches JO - ESAIM: Probability and Statistics PY - 2006 DA - 2006/// SP - 380 EP - 405 VL - 10 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2006016/ UR - https://www.ams.org/mathscinet-getitem?mr=2263072 UR - https://doi.org/10.1051/ps:2006016 DO - 10.1051/ps:2006016 LA - en ID - PS_2006__10__380_0 ER -
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. http://www.numdam.org/articles/10.1051/ps:2006016/
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