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Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2018

Central Limit Theorem for stationary Fleming–Viot particle systems in finite spaces

Abstract

We consider the Fleming–Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its empirical measure converges to the quasistationary distribution of the Markov chain. We complement this Law of Large Numbers with a Central Limit Theorem. Our proof essentially relies on elementary computations on the infinitesimal generator of the Fleming–Viot particle system, and involves the so-called π-return process in the expression of the asymptotic variance. Our work can be seen as an infinite-time version, in the setting of finite space Markov chains, of results by Del Moral and Miclo [ESAIM: Probab. Statist., 2003] and Cérou, Delyon, Guyader and Rousset [arXiv:1611.00515, arXiv:1709.06771].
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Dates and versions

hal-01812120 , version 1 (11-06-2018)
hal-01812120 , version 2 (01-10-2018)

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Cite

Tony Lelièvre, Loucas Pillaud-Vivien, Julien Reygner. Central Limit Theorem for stationary Fleming–Viot particle systems in finite spaces. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, 15, pp.1163-1182. ⟨10.30757/ALEA.v15-43⟩. ⟨hal-01812120v2⟩
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