The Stratonovich heat equation: A continuity result and weak approximations

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

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
Volume18
DOIs
Publication statusPublished - 8 Feb 2013

Keywords

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

Fingerprint Dive into the research topics of 'The Stratonovich heat equation: A continuity result and weak approximations'. Together they form a unique fingerprint.

Cite this