Well-posedness of the martingale problem for super-Brownian motion with interactive branching
arXiv:2303.05832 · doi:10.1016/j.spa.2023.06.006
Abstract
In this paper a martingale problem for super-Brownian motion with interactive branching is derived. The uniqueness of the solution to the martingale problem is obtained by using the pathwise uniqueness of the solution to a corresponding system of SPDEs with proper boundary conditions. The existence of the solution to the martingale problem and the local Hölder continuity of the density process are also studied.