Some properties for superprocess under a stochastic flow
Probability
2015-06-26 v1 Analysis of PDEs
Abstract
For a superprocess under a stochastic flow, we prove that it has a density with respect to the Lebesgue measure for d=1 and is singular for d>1. For d=1, a stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov's L_p-theory for linear SPDE. A snake representation for this superprocess is established. As applications of this representation, we prove the compact support property for general d and singularity of the process when d>1.
Cite
@article{arxiv.math/0606761,
title = {Some properties for superprocess under a stochastic flow},
author = {Kijung Lee and Carl Mueller and Jei Xiong},
journal= {arXiv preprint arXiv:math/0606761},
year = {2015}
}