Convergence of the derivative martingale for the branching random walk in time-inhomogeneous random environment
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914252466421760 |
|---|---|
| author | Hong, Wenming Liang, Shengli |
| author_facet | Hong, Wenming Liang, Shengli |
| contents | Consider a branching random walk on the real line with a random environment in time (BRWRE). A necessary and sufficient condition for the non-triviality of the limit of the derivative martingale is formulated. To this end, we investigate the random walk in time-inhomogeneous random environment (RWRE), which related the BRWRE by the many-to-one formula. The key step is to figure out Tanaka's decomposition for the RWRE conditioned to stay non-negative (or above a line), which is interesting itself as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15204 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of the derivative martingale for the branching random walk in time-inhomogeneous random environment Hong, Wenming Liang, Shengli Probability Primary 60J80, 60K37, secondary 60G42 Consider a branching random walk on the real line with a random environment in time (BRWRE). A necessary and sufficient condition for the non-triviality of the limit of the derivative martingale is formulated. To this end, we investigate the random walk in time-inhomogeneous random environment (RWRE), which related the BRWRE by the many-to-one formula. The key step is to figure out Tanaka's decomposition for the RWRE conditioned to stay non-negative (or above a line), which is interesting itself as well. |
| title | Convergence of the derivative martingale for the branching random walk in time-inhomogeneous random environment |
| topic | Probability Primary 60J80, 60K37, secondary 60G42 |
| url | https://arxiv.org/abs/2306.15204 |