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Stochastic equations of super-Lévy processes with general branching mechanism

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  • He, Hui
  • Li, Zenghu
  • Yang, Xu

Abstract

In this work, the process of distribution functions of a one-dimensional super-Lévy process with general branching mechanism is characterized as the pathwise unique solution of a stochastic integral equation driven by time–space Gaussian white noises and Poisson random measures. This generalizes the recent work of Xiong (2013), where the result for a super-Brownian motion with binary branching mechanism was obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:4:p:1519-1565
    DOI: 10.1016/j.spa.2013.12.007
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    References listed on IDEAS

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    1. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    2. Li, Zenghu & Liu, Huili & Xiong, Jie & Zhou, Xiaowen, 2013. "The reversibility and an SPDE for the generalized Fleming–Viot processes with mutation," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4129-4155.
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    Cited by:

    1. Xiong, Jie & Yang, Xu, 2016. "Superprocesses with interaction and immigration," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3377-3401.
    2. 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.
    3. 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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