Back to Search
Start Over
Weak convergence of the extremes of branching Lévy processes with regularly varying tails.
- Source :
- Journal of Applied Probability; Jun2024, Vol. 61 Issue 2, p622-643, 22p
- Publication Year :
- 2024
-
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 $\mathbb{X}_t$. [ABSTRACT FROM AUTHOR]
- Subjects :
- BRANCHING processes
LEVY processes
LIMIT theorems
ORDER statistics
Subjects
Details
- Language :
- English
- ISSN :
- 00219002
- Volume :
- 61
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Applied Probability
- Publication Type :
- Academic Journal
- Accession number :
- 177041237
- Full Text :
- https://doi.org/10.1017/jpr.2023.103