Fleming-Viot processes : two explicit examples

Bertrand Cloez; Marie-Noémie Thai

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arXiv · 1603.04670

Fleming-Viot processes : two explicit examples

Bertrand Cloez·Marie-Noémie Thai

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Abstract

The purpose of this paper is to extend the investigation of the Fleming-Viot process in discrete space started in a previous work to two specific examples. The first one corresponds to a random walk on the complete graph. Due to its geometry, we establish several explicit and optimal formulas for the Fleming-Viot process (invariant distribution, correlations, spectral gap). The second example corresponds to a Markov chain in a two state space. In this case, the study of the Fleming-Viot particle system is reduced to the study of birth and death process with quadratic rates.

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Bertrand Cloez, Marie-Noémie Thai. 2016-03-15. Fleming-Viot processes : two explicit examples. https://arxiv.org/abs/1603.04670

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