Central Limit Theorem for stationary Fleming--Viot particle systems in finite spaces
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Publication:4962120
zbMATH Open1414.60016arXiv1806.04490MaRDI QIDQ4962120
Author name not available (Why is that?)
Publication date: 30 October 2018
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 -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 C{'e}rou, Delyon, Guyader and Rousset [arXiv:1611.00515, arXiv:1709.06771].
Full work available at URL: https://arxiv.org/abs/1806.04490
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