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


Yang, Hairuo (2023). On the law of terminal value of additive martingales in a remarkable branching stable process. Stochastic Processes and their Applications, 158:361-376.

Abstract

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.

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Modeling and Simulation
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied Mathematics, Modeling and Simulation, Statistics and Probability primary 60G44; 60J80 Branching random walk, Additive martingale, Branching stable processes, Smoothing transforms
Language:English
Date:1 April 2023
Deposited On:09 Jan 2024 11:20
Last Modified:30 Jun 2024 01:36
Publisher:Elsevier
ISSN:0304-4149
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.spa.2023.01.005
Project Information:
  • : FunderSNSF
  • : Grant ID188693
  • : Project TitleGrowth-Fragmentations and Beyond
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)