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The probabilities of extinction in a branching random walk on a strip
| Content Provider | Scilit |
|---|---|
| Author | Braunsteins, Peter Hautphenne, Sophie |
| Copyright Year | 2020 |
| Description | We consider a class of multitype Galton–Watson branching processes with a countably infinite type set $\mathcal{X}_d$ whose mean progeny matrices have a block lower Hessenberg form. For these processes, we study the probabilities $\textbf{\textit{q}}(A)$ of extinction in sets of types $A\subseteq \mathcal{X}_d$ . We compare $\textbf{\textit{q}}(A)$ with the global extinction probability $\textbf{\textit{q}} = \textbf{\textit{q}}(\mathcal{X}_d)$ , that is, the probability that the population eventually becomes empty, and with the partial extinction probability $\tilde{\textbf{\textit{q}}}$ , that is, the probability that all types eventually disappear from the population. After deriving partial and global extinction criteria, we develop conditions for $\textbf{\textit{q}} < \textbf{\textit{q}}(A) < \tilde{\textbf{\textit{q}}}$ . We then present an iterative method to compute the vector $\textbf{\textit{q}}(A)$ for any set A. Finally, we investigate the location of the vectors $\textbf{\textit{q}}(A)$ in the set of fixed points of the progeny generating vector. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C69BB72B6B4A0CDEA7324E21BA97BC4E/S0021900220000352a.pdf/div-class-title-the-probabilities-of-extinction-in-a-branching-random-walk-on-a-strip-div.pdf |
| Ending Page | 831 |
| Page Count | 21 |
| Starting Page | 811 |
| ISSN | 00219002 |
| e-ISSN | 14756072 |
| DOI | 10.1017/jpr.2020.35 |
| Journal | Journal of applied probability |
| Issue Number | 3 |
| Volume Number | 57 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2020-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of applied probability Mathematical Physics type Branching Process Extinction Probability Fixed Point |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
