Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Some properties of superprocesses under a stochastic flow

Kijung Lee, Carl Mueller, and Jie Xiong

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 2 (2009), 477-490.

Dates
First available in Project Euclid: 29 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1241024677

Digital Object Identifier
doi:10.1214/08-AIHP171

Mathematical Reviews number (MathSciNet)
MR2521410

Zentralblatt MATH identifier
1171.60011

Subjects
Primary: 60G57: Random measures 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Superprocess Random environment Snake representation Stochastic partial differential equation

Citation

Lee, Kijung; Mueller, Carl; Xiong, Jie. Some properties of superprocesses under a stochastic flow. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 2, 477--490. doi:10.1214/08-AIHP171. https://projecteuclid.org/euclid.aihp/1241024677


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