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Rough Burgers-like equations with multiplicative noise
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Hairer, Martin and Weber, Hendrik (2013) Rough Burgers-like equations with multiplicative noise. Probability Theory and Related Fields, Volume 155 (Number 1-2). pp. 71-126. doi:10.1007/s00440-011-0392-1 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-011-0392-1
Abstract
We construct solutions to vector valued Burgers type equations perturbed by a multiplicative space–time white noise in one space dimension. Due to the roughness of the driving noise, solutions are not regular enough to be amenable to classical methods. We use the theory of controlled rough paths to give a meaning to the spatial integrals involved in the definition of a weak solution. Subject to the choice of the correct reference rough path, we prove unique solvability for the equation and we show that our solutions are stable under smooth approximations of the driving noise.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | White noise theory, Probabilities, Integrals, Approximation theory, Stochastic partial differential equations | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | February 2013 | ||||
Dates: |
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Volume: | Volume 155 | ||||
Number: | Number 1-2 | ||||
Page Range: | pp. 71-126 | ||||
DOI: | 10.1007/s00440-011-0392-1 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Royal Society (Great Britain), Leverhulme Trust (LT) | ||||
Grant number: | EP/D071593/1 (EPSRC) | ||||
Version or Related Resource: | Erratum: Hairer, M. and Weber, H. (2013). Rough Burgers-like equations with multiplicative noise. Probability Theory and Related Fields, 157(3-4), pp. 1011-1013. | ||||
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