Rough Burgers-like equations with multiplicative noise

Martin Hairer, Hendrik Weber

Research output: Contribution to journalArticle

25 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)71-126
Number of pages56
JournalProbability Theory and Related Fields
Volume155
Issue number1-2
DOIs
Publication statusPublished - 1 Feb 2013

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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