Cooperative birth processes with linear or sublinear intensity
type: Item
instance of: scholarly article
title: Cooperative birth processes with linear or sublinear intensity
zbMATH Open document ID: 0546.60074
DOI: 10.1016/0304-4149(84)90007-3
author: Petra Küster
published in: Stochastic Processes and their Applications
publication date: 1984-01-01T00:00:00Z
review text: The asymptotic behavior of an increasing Markov process \(\{Z_ t,t\in {\mathbb{R}}^+\}\), \(Z_ t=(Z_ t(1),...,Z_ t(n))\in {\mathbb{N}}^ n\), is investigated. The increments are i.i.d. with finite expectation and covariances. Given \(Z_ t\), the time until the next jump is exponentially distributed with intensity \(h(Z_ t/| Z_ t|)f(Z_ t)\), where h and f are sufficiently smooth positive functions and \(| Z_ t| =\sum^{n}_{j=1}Z_ t(j)\). While a linear f results in asymptotically exponential growth, a suitable class of sublinear f leads to a growth at most that of a power. Covering both cases, analogues of the strong LLN, the CLT and LIL are obtained.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3870357
zbMATH Keywords: birth process
zbMATH Keywords: central limit theorem
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: growth rate
MaRDI profile type: Publication
full work available at URL: 0304-4149(84)90007-3
OpenAlex ID: W2064095247
cites work: Q5812603
cites work: Almost Sure Behavior of Linear Functionals of Supercritical Branching Processes
cites work: On some two-sex population models
cites work: Q5557517
cites work: The asymptotic behaviour of birth and death and some related processes
cites work: Quadratic transformations: a model for population growth. II
cites work: Some nonlinear stochastic growth models
cites work: Limit theorems for stochastic growth models. II
cites work: Extinction probability, regularity and asymptotic growth of Markovian populations
cites work: Modes of growth of counting processes with increasing arrival rates
cites work: Asymptotic growth of a class of size-and-age-dependent birth processes
description: scientific article; zbMATH DE number 3870357