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Some properties for superprocess under a stochastic flow

Kijung Lee·Carl Mueller·Jei Xiong
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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.

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Kijung Lee, Carl Mueller, Jei Xiong. 2006-06-29. Some properties for superprocess under a stochastic flow. https://doi.org/10.1214/08-aihp171

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