Advances in Applied Probability

Asymptotic bahavior of the Moran particle system

Shui Feng and Jie Xiong

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 45, Number 2 (2013), 379-397.

Dates
First available in Project Euclid: 10 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1370870123

Digital Object Identifier
doi:10.1239/aap/1370870123

Mathematical Reviews number (MathSciNet)
MR3102456

Zentralblatt MATH identifier
1271.60103

Subjects
Primary: 60F10: Large deviations
Secondary: 92D10: Genetics {For genetic algebras, see 17D92}

Keywords
Exponential tightness Moran particle process Fleming-Viot process genealogy large deviations particle representation

Citation

Feng, Shui; Xiong, Jie. Asymptotic bahavior of the Moran particle system. Adv. in Appl. Probab. 45 (2013), no. 2, 379--397. doi:10.1239/aap/1370870123. https://projecteuclid.org/euclid.aap/1370870123


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