Law of large numbers for superdiffusions : the non-ergodic case
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 1, pp. 1-6.

Dans un travail précédent, l'auteur, D. Turaev et A. Winter, ont prouvé la Loi des Grand Nombres pour la masse locale de certaines diffusions sous une hypothèse d'ergodicité. Dans cet article nous allons au delà de l'ergodicité, plus précisement nous considérons des cas où le scaling de l'espérance de la masse locale n'est pas purement exponentiel. Entre autres, nous prouvons l'analogue de la LGN de Watanabe-Biggins pour le super mouvement brownien.

In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe-Biggins LLN for super-brownian motion.

DOI : 10.1214/07-AIHP156
Classification : 60J60, 60J80
Mots-clés : super-brownian motion, superdiffusion, superprocess, law of large numbers, H-transform, weighted superprocess, scaling limit, local extinction 
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Engländer, János. Law of large numbers for superdiffusions : the non-ergodic case. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 1, pp. 1-6. doi : 10.1214/07-AIHP156. http://www.numdam.org/articles/10.1214/07-AIHP156/

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