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Uniform in time propagation of chaos for a Moran model

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  • Cloez, Bertrand
  • Corujo, Josué

Abstract

This article studies the limit of the empirical distribution induced by a mutation-selection multi-allelic Moran model. Our results include a uniform in time bound for the propagation of chaos in Lp of order N, and the proof of the asymptotic normality with zero mean and explicit variance, when the number of individuals tend towards infinity, for the approximation error between the empirical distribution and its limit. Additionally, we explore the interpretation of this Moran model as a particle process whose empirical probability measure approximates a quasi-stationary distribution, in the same spirit as the Fleming–Viot particle systems.

Suggested Citation

  • Cloez, Bertrand & Corujo, Josué, 2022. "Uniform in time propagation of chaos for a Moran model," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 251-285.
    • Handle: RePEc:eee:spapps:v:154:y:2022:i:c:p:251-285
    DOI: 10.1016/j.spa.2022.09.006
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    References listed on IDEAS

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    1. P. Moral & F. Patras & S. Rubenthaler, 2011. "Convergence of U-Statistics for Interacting Particle Systems," Journal of Theoretical Probability, Springer, vol. 24(4), pages 1002-1027, December.
    2. Cloez, Bertrand & Thai, Marie-Noémie, 2016. "Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 680-702.
    3. Moral, P. Del & Miclo, L., 2000. "A Moran particle system approximation of Feynman-Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 193-216, April.
    4. Ren, Yao-Feng & Liang, Han-Ying, 2001. "On the best constant in Marcinkiewicz-Zygmund inequality," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 227-233, June.
    5. Angeli, Letizia & Grosskinsky, Stefan & Johansen, Adam M., 2021. "Limit theorems for cloning algorithms," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 117-152.
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