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.
Publié le : 2009-05-15
Classification:
Superprocess,
Random environment,
Snake representation,
Stochastic partial differential equation,
60G57,
60H15,
60J80
@article{1241024677,
author = {Lee, Kijung and Mueller, Carl and Xiong, Jie},
title = {Some properties of superprocesses under a stochastic flow},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 477-490},
language = {en},
url = {http://dml.mathdoc.fr/item/1241024677}
}
Lee, Kijung; Mueller, Carl; Xiong, Jie. Some properties of superprocesses under a stochastic flow. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 477-490. http://gdmltest.u-ga.fr/item/1241024677/