Publication: On the law of terminal value of additive martingales in a remarkable branching stable process
On the law of terminal value of additive martingales in a remarkable branching stable process
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Yang, H. (2023). On the law of terminal value of additive martingales in a remarkable branching stable process. Stochastic Processes and Their Applications, 158, 361–376. https://doi.org/10.1016/j.spa.2023.01.005
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We give an explicit description of the law of terminal value 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 as . These are in sharp contrast with results in the literature such as Liu (2000, 2001) and Buraczewski (2009). We further show that the law of is self-decomposable, and therefore, possesses a unimodal density. We specify the asymptotic behavior at 0 and at of the latter.
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- Yang, Hairuo
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Yang, H. (2023). On the law of terminal value of additive martingales in a remarkable branching stable process. Stochastic Processes and Their Applications, 158, 361–376. https://doi.org/10.1016/j.spa.2023.01.005
