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On the law of terminal value of additive martingales in a remarkable branching stable process

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  • Yang, Hairuo

Abstract

We give an explicit description of the law of terminal value W of additive martingales in a remarkable branching stable process. We show that the right tail probability of the terminal value decays exponentially fast and the left tail probability follows that −logP(W

Suggested Citation

  • Yang, Hairuo, 2023. "On the law of terminal value of additive martingales in a remarkable branching stable process," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 361-376.
    • Handle: RePEc:eee:spapps:v:158:y:2023:i:c:p:361-376
    DOI: 10.1016/j.spa.2023.01.005
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    References listed on IDEAS

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    1. Gerold Alsmeyer & Bastien Mallein, 2022. "A Simple Method to Find All Solutions to the Functional Equation of the Smoothing Transform," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2569-2599, December.
    2. Buraczewski, Dariusz, 2009. "On tails of fixed points of the smoothing transform in the boundary case," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3955-3961, November.
    3. Anthony G. Pakes, 2020. "Self-Decomposable Laws from Continuous Branching Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 361-395, March.
    4. Liu, Quansheng, 2001. "Asymptotic properties and absolute continuity of laws stable by random weighted mean," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 83-107, September.
    5. Liu, Quansheng, 2000. "On generalized multiplicative cascades," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 263-286, April.
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