# Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder

Abstract : We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable as the smoothing parameter vanishes. In this regime, we study the rate of convergence and show that the pointwise fluctuations of the smoothened solutions as well as that of the underlying martingale of the Brownian directed polymer converge to a Gaussian limit.
Keywords :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

Littérature citée [6 références]

https://hal.archives-ouvertes.fr/hal-01837908
Contributeur : Clement Cosco <>
Soumis le : jeudi 12 juillet 2018 - 23:48:11
Dernière modification le : mardi 19 mars 2019 - 01:23:28
Document(s) archivé(s) le : lundi 15 octobre 2018 - 12:40:58

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ConvRateSHE_J10.pdf
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### Identifiants

• HAL Id : hal-01837908, version 1
• ARXIV : 1807.03902

### Citation

Francis Comets, Clément Cosco, Chiranjib Mukherjee. Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder. 2018. 〈hal-01837908〉

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