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Rough Burgers-like equations with multiplicative noise
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  • Published: 27 October 2011

Rough Burgers-like equations with multiplicative noise

  • Martin Hairer1 &
  • Hendrik Weber1 

Probability Theory and Related Fields volume 155, pages 71–126 (2013)Cite this article

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An Erratum to this article was published on 30 October 2013

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.

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Authors and Affiliations

  1. Mathematics Department, University of Warwick, Coventry, CV4 7AL, UK

    Martin Hairer & Hendrik Weber

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  1. Martin Hairer
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  2. Hendrik Weber
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Correspondence to Martin Hairer.

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Hairer, M., Weber, H. Rough Burgers-like equations with multiplicative noise. Probab. Theory Relat. Fields 155, 71–126 (2013). https://doi.org/10.1007/s00440-011-0392-1

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  • Received: 06 December 2010

  • Revised: 29 September 2011

  • Published: 27 October 2011

  • Issue Date: February 2013

  • DOI: https://doi.org/10.1007/s00440-011-0392-1

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Mathematics Subject Classification (2010)

  • 60H15
  • 35R60
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