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Asymptotic Bahavior of the Moran Particle System

Part of: Limit theorems

Published online by Cambridge University Press:  22 February 2016

Shui Feng  and
Jie Xiong
Shui Feng*
Affiliation:
McMaster University
Jie Xiong*
Affiliation:
University of Macau and University of Tennessee
*
∗ Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton Hall #211, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada. Email address: shuifeng@univmail.cis.mcmaster.ca
∗∗ Postal address: Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, China.
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Abstract

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The asymptotic behavior is studied for an interacting particle system that involves independent motion and random sampling. For a fixed sampling rate, the empirical process of the particle system converges to the Fleming-Viot process when the number of particles approaches ∞. If the sampling rate approaches 0 as the number of particles becomes large, the corresponding empirical process will converge to the deterministic flow of the motion. In the main results of this paper, we study the corresponding central limit theorems and large deviations. Both the Gaussian limits and the large deviations depend on the sampling scales explicitly.

Keywords

Exponential tightnessMoran particle processFleming-Viot processgenealogylarge deviationsparticle representation

MSC classification

Primary: 60F10: Large deviations
Secondary: 92D10: Genetics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 2 , June 2013 , pp. 379 - 397
Copyright
© Applied Probability Trust 

Footnotes

Research supported by the Natural Science and Engineering Research Council of Canada.

Research partially supported by NSF DMS-0906907.

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