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Well-posedness of the martingale problem for super-Brownian motion with interactive branching

Author

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  • Ji, Lina
  • Xiong, Jie
  • Yang, Xu

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.

Suggested Citation

  • Ji, Lina & Xiong, Jie & Yang, Xu, 2023. "Well-posedness of the martingale problem for super-Brownian motion with interactive branching," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 288-322.
    • Handle: RePEc:eee:spapps:v:163:y:2023:i:c:p:288-322
    DOI: 10.1016/j.spa.2023.06.006
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    References listed on IDEAS

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    1. Xiong, Jie & Yang, Xu, 2016. "Superprocesses with interaction and immigration," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3377-3401.
    2. He, Hui & Li, Zenghu & Yang, Xu, 2014. "Stochastic equations of super-Lévy processes with general branching mechanism," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1519-1565.
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    1. Xiong, Jie & Yang, Xu, 2016. "Superprocesses with interaction and immigration," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3377-3401.
    2. Xiong, Jie & Yang, Xu, 2019. "Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2681-2722.

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