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Abstract: We consider a class of singular perturbations to the stochastic heat equationor semilinear variations thereof. The interesting feature of theseperturbations is that, as the small parameter epsilon tends to zero, theirsolutions converge to the -wrong- limit, i.e. they do not converge to thesolution obtained by simply setting epsilon = 0. A similar effect is alsoobserved for some formally small stochastic perturbations of a deterministicsemilinear parabolic PDE.Our proofs are based on a detailed analysis of the spatially rough componentof the equations, combined with a judicious use of Gaussian concentrationinequalities.



Author: Martin Hairer

Source: https://arxiv.org/



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