Probability Theory and Related Fields

, Volume 155, Issue 1–2, pp 71–126 | Cite as

Rough Burgers-like equations with multiplicative noise

Article

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.

Mathematics Subject Classification (2010)

60H15 35R60 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of WarwickCoventryUK

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