Article contents
Weak convergence of the extremes of branching Lévy processes with regularly varying tails
Published online by Cambridge University Press: 06 December 2023
Abstract
We study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized,
$\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order statistics of
$\mathbb{X}_t$.
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240504053549869-0494:S0021900223001031:S0021900223001031_inline684.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240504053549869-0494:S0021900223001031:S0021900223001031_inline685.png?pub-status=live)
- 1
- Cited by