Some properties for superprocess under a stochastic flow

Details Some properties for superprocess under a stochastic flow Some properties for superprocess under a stochastic flow

2006-06-29

arxiv.org/abs/math/0606761v1

Ann. Poincare, 45, 2, 477-490 (2009)

Mathematics

Probability

Scientific paper

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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