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

Abstract

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We study strictly parabolic stochastic partial differential equations on 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.


How to cite

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Ferrante, 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 -

References

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