Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour
Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, pp. 194-206.

We consider the solution to the parabolic Anderson model with homogeneous initial condition in large time-dependent boxes. We derive stable limit theorems, ranging over all possible scaling parameters, for the rescaled sum over the solution depending on the growth rate of the boxes. Furthermore, we give sufficient conditions for a strong law of large numbers.

Nous considérons la solution du modèle parabolique d’Anderson avec condition initiale homogène sur de grandes boîtes dépendantes du temps. Nous dérivons des théorèmes limites stables, pour toutes les valeurs possibles des paramètres d’échelle, pour la somme de la solution changée d’échelle en fonction du taux de croissance des boîtes. De plus, nous donnons des conditions suffisantes pour une loi des grands nombres.

DOI: 10.1214/13-AIHP574
Classification: 60K37,  82C44,  60H25,  60F05
Keywords: parabolic Anderson model, stable limit laws, strong law of large numbers
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Gärtner, Jürgen; Schnitzler, Adrian. Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, pp. 194-206. doi : 10.1214/13-AIHP574. http://www.numdam.org/articles/10.1214/13-AIHP574/

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