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Central limit approximations for Markov population processes with countably many types


 
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1. Title Title of document Central limit approximations for Markov population processes with countably many types
 
2. Creator Author's name, affiliation, country Andrew Barbour; Universität Zürich; Switzerland
 
2. Creator Author's name, affiliation, country Malwina Luczak; University of Sheffield; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Epidemic models; metapopulation processes; countably many types; central limit approximation; Markov population processes
 
3. Subject Subject classification 92D30; 60J27; 60B12
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Australian Research Council (ARC); Engineering and Physical Sciences Research Council (EPSRC)
 
7. Date (YYYY-MM-DD) 2012-10-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1760
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1760
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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