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May 2009 Some properties of superprocesses under a stochastic flow
Kijung Lee, Carl Mueller, Jie Xiong
Ann. Inst. H. Poincaré Probab. Statist. 45(2): 477-490 (May 2009). DOI: 10.1214/08-AIHP171

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.

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.

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Kijung Lee. Carl Mueller. Jie Xiong. "Some properties of superprocesses under a stochastic flow." Ann. Inst. H. Poincaré Probab. Statist. 45 (2) 477 - 490, May 2009. https://doi.org/10.1214/08-AIHP171

Information

Published: May 2009
First available in Project Euclid: 29 April 2009

zbMATH: 1171.60011
MathSciNet: MR2521410
Digital Object Identifier: 10.1214/08-AIHP171

Subjects:
Primary: 60G57 , 60H15
Secondary: 60J80

Keywords: random environment , Snake representation , Stochastic partial differential equation , Superprocess

Rights: Copyright © 2009 Institut Henri Poincaré

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Vol.45 • No. 2 • May 2009
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