A distribution-function-valued SPDE and its applications (Q340358)

\textit{J. Xiong} [Ann. Probab. 41, No. 2, 1030--1054 (2013; Zbl 1266.60119)] studied the strong existence and uniqueness for an SPDE for the distribution-function process of a measure-valued super-Brownian motion. The authors improve theses results.NEWLINENEWLINEThey establish a comparison theorem and, under localized conditions on the coefficients, they show that the solution is distribution-function-valued. The pathwise uniqueness of the solution is also established.NEWLINENEWLINEUsing these results, the martingale problems for an interacting super-Brownian motion and an interacting Fleming-Viot process are shown to be well-posed. The existence of solutions to the martingale problems follows from the relationship with their corresponding SPDEs and the existence of solutions of these SPDEs. Finally, the authors study the existence of density fields and survival-extinction behaviors of the interacting super-Brownian motions and Fleming-Viot processes.