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1 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine 2 Departament de Matemàtiques 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.

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





Author: Aurélien Deya - Maria Jolis - Lluís Quer-Sardanyons -

Source: https://hal.archives-ouvertes.fr/



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