Some properties of superprocesses under a stochastic flow
Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 2, pp. 477-490.

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.

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.

DOI: 10.1214/08-AIHP171
Classification: 60G57,  60H15,  60J80
Keywords: superprocess, random environment, snake representation, stochastic partial differential equation
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Lee, Kijung; Mueller, Carl; Xiong, Jie. Some properties of superprocesses under a stochastic flow. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 2, pp. 477-490. doi : 10.1214/08-AIHP171. http://www.numdam.org/articles/10.1214/08-AIHP171/

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