The Stratonovich heat equation: a continuity result and weak approximations

Aurélien Deya (Institut Élie Cartan, Nancy)
Maria Jolis (Universitat Autònoma de Barcelona)
Lluís Quer-Sardanyons (Universitat Autònoma de Barcelona)

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.

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Pages: 1-34

Publication Date: January 6, 2013

DOI: 10.1214/EJP.v18-2004

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