Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774076 | Journal of Differential Equations | 2017 | 34 Pages |
Abstract
In this paper we further study the stochastic partial differential equation first proposed by Xiong [22]. Under localized conditions on its coefficients, we prove a comparison theorem on its solutions and show that the solution is in fact distribution-function-valued. We also establish pathwise uniqueness of the solution. As applications we obtain the well-posedness of martingale problems for two classes of measure-valued diffusions: interacting super-Brownian motions and interacting Fleming-Viot processes. Properties of the two superprocesses such as the existence of density fields and the survival-extinction behaviors are also studied.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Li Wang, Xu Yang, Xiaowen Zhou,