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2013 The Stratonovich heat equation: a continuity result and weak approximations
Aurélien Deya, Maria Jolis, Lluís Quer-Sardanyons
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Electron. J. Probab. 18: 1-34 (2013). DOI: 10.1214/EJP.v18-2004


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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Aurélien Deya. Maria Jolis. Lluís Quer-Sardanyons. "The Stratonovich heat equation: a continuity result and weak approximations." Electron. J. Probab. 18 1 - 34, 2013.


Accepted: 6 January 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1311.60067
MathSciNet: MR3024097
Digital Object Identifier: 10.1214/EJP.v18-2004

Primary: 60H10
Secondary: 60H05 , 60H07

Keywords: convergence in law , convolutional rough paths theory , Stochastic heat equation , Stratonovich integral

Vol.18 • 2013
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