Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour
Gärtner, Jürgen ; Schnitzler, Adrian
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015), p. 194-206 / Harvested from Numdam
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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.

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.

Publié le : 2015-01-01
DOI : https://doi.org/10.1214/13-AIHP574
Classification:  60K37,  82C44,  60H25,  60F05 
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     author = {G\"artner, J\"urgen and Schnitzler, Adrian},
     title = {Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {51},
     year = {2015},
     pages = {194-206},
     doi = {10.1214/13-AIHP574},
     mrnumber = {3300968},
     zbl = {06412902},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2015__51_1_194_0}
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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, Tome 51 (2015) pp. 194-206. doi : 10.1214/13-AIHP574. http://gdmltest.u-ga.fr/item/AIHPB_2015__51_1_194_0/

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