Header

UZH-Logo

Maintenance Infos

Central limit approximations for Markov population processes with countably many types


Barbour, A D; Luczak, Malwina (2012). Central limit approximations for Markov population processes with countably many types. Electronic Journal of Probability, 17(90):1-16.

Abstract

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.

Abstract

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.

Statistics

Citations

Dimensions.ai Metrics
1 citation in Web of Science®
2 citations in Scopus®
3 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

1 download since deposited on 28 Dec 2017
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2012
Deposited On:28 Dec 2017 14:38
Last Modified:18 Apr 2018 11:49
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Funders:Schweizerischer Nationalfonds
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v17-1760

Download

Download PDF  'Central limit approximations for Markov population processes with countably many types'.
Preview
Content: Published Version
Language: English
Filetype: PDF
Size: 276kB
View at publisher