SPDEs with coloured noise: Analytic and stochastic approaches
Marco Ferrante; Marta Sanz-Solé
ESAIM: Probability and Statistics (2006)
- Volume: 10, page 380-405
- ISSN: 1292-8100
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topFerrante, Marco, and Sanz-Solé, Marta. "SPDEs with coloured noise: Analytic and stochastic approaches." ESAIM: Probability and Statistics 10 (2006): 380-405. <http://eudml.org/doc/249763>.
@article{Ferrante2006,
abstract = { We study strictly
parabolic stochastic partial differential equations on $\mathbb\{R\}^d$, 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.
},
author = {Ferrante, Marco, Sanz-Solé, Marta},
journal = {ESAIM: Probability and Statistics},
keywords = {Stochastic partial differential equations; mild and weak solutions;
random noise.; stochastic partial differential equations; random noise},
language = {eng},
month = {10},
pages = {380-405},
publisher = {EDP Sciences},
title = {SPDEs with coloured noise: Analytic and stochastic approaches},
url = {http://eudml.org/doc/249763},
volume = {10},
year = {2006},
}
TY - JOUR
AU - Ferrante, Marco
AU - Sanz-Solé, Marta
TI - SPDEs with coloured noise: Analytic and stochastic approaches
JO - ESAIM: Probability and Statistics
DA - 2006/10//
PB - EDP Sciences
VL - 10
SP - 380
EP - 405
AB - We study strictly
parabolic stochastic partial differential equations on $\mathbb{R}^d$, 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.
LA - eng
KW - Stochastic partial differential equations; mild and weak solutions;
random noise.; stochastic partial differential equations; random noise
UR - http://eudml.org/doc/249763
ER -
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