Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2503.03580 |
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Inhaltsangabe:
- In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed Lévy process $X$ in $\mathbb{R}$. Let $ζ$ denote the extinction time, $M_t$ be the maximal position of all the particles alive at time $t$, and $M:=\sup_{t\ge 0}M_t$ be the all-time maximum. Under the assumption that the offspring distribution satisfies the $L\log L$ condition and some conditions on the spatial motion, we find the decay rate of the survival probability $\mathbb{P}_x(ζ>t)$ and the tail behavior of $M_t$ as $t\to\infty$. As a consequence, we establish a Yaglom-type theorem. We also find the asymptotic behavior of $\mathbb{P}_x(M>y)$ as $y\to\infty$.