# 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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