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Dynamics of a Fleming–Viot type particle system on the cycle graph

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  • Corujo, Josué

Abstract

We study the Fleming–Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is non-reversible with non-explicit invariant distribution. Our main results include quantitative propagation of chaos and exponential ergodicity with explicit constants, as well as formulas for covariances at equilibrium in terms of the Chebyshev polynomials. We also obtain a bound uniform in time for the convergence of the proportion of particles in each state when the number of particles goes to infinity.

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  • Corujo, Josué, 2021. "Dynamics of a Fleming–Viot type particle system on the cycle graph," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 57-91.
    • Handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:57-91
    DOI: 10.1016/j.spa.2021.02.001
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    References listed on IDEAS

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    1. 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.
    2. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    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. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
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