Lee, Kijung; Mueller, Carl; Xiong, Jie
Some properties of superprocesses under a stochastic flow
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 2 , p. 477-490
Zbl 1171.60011 | MR 2521410
doi : 10.1214/08-AIHP171
URL stable : http://www.numdam.org/item?id=AIHPB_2009__45_2_477_0

Classification:  60G57,  60H15,  60J80
Nous montrons que, sous un flot stochastique en dimension un, un superprocess a une densité par rapport à la mesure de Lebesgue. Nous déduisons une équation différentielle stochastique satisfaite par la densité. Nous montrons ensuite la régularité de la solution en utilisant la theorie de Krylov pour les EDPS linéaires dans Lp.
For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov's Lp-theory for linear SPDE.

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