Extinction in lower Hessenberg branching processes with countably many types
| Autor: | Sophie Hautphenne, Peter Braunsteins |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
extinction criterion growth random-walks rates Second moment of area galton-watson process Fixed point Type (model theory) survival 01 natural sciences Combinatorics 010104 statistics & probability 60J05 FOS: Mathematics Quantitative Biology::Populations and Evolution 60J22 Continuum (set theory) 0101 mathematics Mathematics Sequence 60J80 varying environment Probability (math.PR) 010102 general mathematics Generating function Random walk Physics::Classical Physics Galton–Watson process fixed point Physics::Space Physics extinction probability Statistics Probability and Uncertainty Mathematics - Probability Infinite-type branching process |
| Zdroj: | Ann. Appl. Probab. 29, no. 5 (2019), 2782-2818 |
| ISSN: | 2782-2818 |
| Popis: | We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton–Watson processes with typeset $\mathcal{X}=\{0,1,2,\ldots\}$, in which individuals of type $i$ may give birth to offspring of type $j\leq i+1$ only. For this class of processes, we study the set $S$ of fixed points of the progeny generating function. In particular, we highlight the existence of a continuum of fixed points whose minimum is the global extinction probability vector $\boldsymbol{q}$ and whose maximum is the partial extinction probability vector $\boldsymbol{\tilde{q}}$. In the case where $\boldsymbol{\tilde{q}}=\boldsymbol{1}$, we derive a global extinction criterion which holds under second moment conditions, and when $\boldsymbol{\tilde{q}} |
| Databáze: | OpenAIRE |
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