Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909724111273984 |
|---|---|
| author | Collet, Pierre Méléard, Sylvie San, Jaime |
| author_facet | Collet, Pierre Méléard, Sylvie San, Jaime |
| contents | In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three regimes, critical, subcritical and supercritical. Under suitable hypotheses on the Feynman-Kac semigroup, we prove a new recurrence for the moments and the extinction probability, their time asymptotics and the convergence in law for the measure-valued birth and death process conditioned to non extinction, leading to the existence of Q-process and Yaglom limit (in this infinite dimensional setting). We develop three classes of natural examples where our results apply. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes Collet, Pierre Méléard, Sylvie San, Jaime Probability In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three regimes, critical, subcritical and supercritical. Under suitable hypotheses on the Feynman-Kac semigroup, we prove a new recurrence for the moments and the extinction probability, their time asymptotics and the convergence in law for the measure-valued birth and death process conditioned to non extinction, leading to the existence of Q-process and Yaglom limit (in this infinite dimensional setting). We develop three classes of natural examples where our results apply. |
| title | Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2508.04089 |