Large and moderate deviations for the total population arising from a sub-critical Galton-Watson process with immigration
type: Item
instance of: scholarly article
title: Large and moderate deviations for the total population arising from a sub-critical Galton-Watson process with immigration
zbMATH Open document ID: 1392.60071
author: Shihang Yu
author: Xia Chen
author: Dehui Wang
published in: Journal of Theoretical Probability
publication date: 2018-04-20T00:00:00Z
review text: Define a Galton-Watson process with immigration by the following relation \[ N_k = \sum_{j=1}^{N_k-1} \xi_{k-1,j} + \varepsilon_k, \] with i.i.d. offspring variables \(\xi_{k,j}\) and independent sequence of i.i.d. immigration variables \(\varepsilon_k\); with generic copies \(\xi\) and \(\varepsilon\), respectively. Assuming subcriticality \(E \xi < 1\) as well as finite exponential moments for \(\xi\) and \(\varepsilon\), the authors prove large and moderate deviation principles for empirical mean of the population size \[ \frac{N_1 + \dots + N_n}{n}, \] i.e., the empirical mean size of the generations \(1, \dots, n\).
reviewed by: Sebastian Mentemeier
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 6862617
zbMATH Keywords: branching process with immigration
zbMATH Keywords: integer-valued AR model
zbMATH Keywords: large deviations principle
zbMATH Keywords: moderate deviation principle
MaRDI profile type: Publication
full work available at URL: s10959-016-0706-4
OpenAlex ID: W2477374060
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DOI: 10.1007/S10959-016-0706-4
description: scientific article; zbMATH DE number 6862617