The Stratonovich heat equation: A continuity result and weak approximations

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14 Citations (Scopus)


We consider a Stratonovich heat equation in (0, 1) with a nonlinear multiplicative noise driven by a trace-class Wiener process. First, the equation is shown to have a unique mild solution. Secondly, convolutional rough paths techniques are used to provide an almost sure continuity result for the solution with respect to the solution of the 'smooth' equation obtained by replacing the noise with an absolutely continuous process. This continuity result is then exploited to prove weak convergence results based on Donsker and Kac-Stroock type approximations of the noise.
Original languageEnglish
JournalElectronic Journal of Probability
Publication statusPublished - 8 Feb 2013


  • Convergence in law
  • Convolutional rough paths theory
  • Stochastic heat equation
  • Stratonovich integral


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