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PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES

Part of: Stochastic analysis Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  14 August 2015

MASSIMILIANO GUBINELLI ,
PETER IMKELLER  and
NICOLAS PERKOWSKI
MASSIMILIANO GUBINELLI
Affiliation:
CEREMADE & CNRS UMR 7534, Université Paris-Dauphine and Institut Universitaire de France, France; gubinelli@ceremade.dauphine.fr
PETER IMKELLER
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Germany; imkeller@math.hu-berlin.de
NICOLAS PERKOWSKI
Affiliation:
CEREMADE & CNRS UMR 7534, Université Paris-Dauphine, France; perkowski@ceremade.dauphine.fr

Abstract

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We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems such as differential equations driven by fractional Brownian motion, a fractional Burgers-type stochastic PDE (SPDE) driven by space-time white noise, and a nonlinear version of the parabolic Anderson model with a white noise potential.

MSC classification

Primary: 60H15: Stochastic partial differential equations
Secondary: 35S50: Paradifferential operators
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 3 , 2015 , e6
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2015

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