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arXiv · 2303.05832

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 H\"{o}lder continuity of the density process are also studied.

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Lina Ji, Jie Xiong, Xu Yang. 2023-03-10. Well-posedness of the martingale problem for super-Brownian motion with interactive branching. https://doi.org/10.1016/j.spa.2023.06.006

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