2023•arXiv (Cornell University)Open access
Well-posedness of the martingale problem for super-Brownian motion with interactive branching
Lina Ji, Jie Xiong, Xu Yang
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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.
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