Multitype branching processes in random environments with not strictly positive expectation matrices
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910306145402880 |
|---|---|
| author | Orgoványi, Vilma Simon, Károly |
| author_facet | Orgoványi, Vilma Simon, Károly |
| contents | It is well known that under some conditions the almost sure survival probability of a multitype branching processes in random environment is positive if the Lyapunov exponent corresponding to the expectation matrices is positive, and zero if the Lyapunov exponent is negative. The goal of this note is to establish similar results when certain positivity conditions on the expectation matrices are not met. One application of such a result is to classify the positivity of Lebesgue measure of certain overlapping random self-similar sets in the line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multitype branching processes in random environments with not strictly positive expectation matrices Orgoványi, Vilma Simon, Károly Probability Dynamical Systems 60J80, 60J85 (Primary) 28A80 (Secondary) It is well known that under some conditions the almost sure survival probability of a multitype branching processes in random environment is positive if the Lyapunov exponent corresponding to the expectation matrices is positive, and zero if the Lyapunov exponent is negative. The goal of this note is to establish similar results when certain positivity conditions on the expectation matrices are not met. One application of such a result is to classify the positivity of Lebesgue measure of certain overlapping random self-similar sets in the line. |
| title | Multitype branching processes in random environments with not strictly positive expectation matrices |
| topic | Probability Dynamical Systems 60J80, 60J85 (Primary) 28A80 (Secondary) |
| url | https://arxiv.org/abs/2401.12767 |