Section: New Results

Adaptive multilevel splitting as a Fleming–Viot system

Participants : Frédéric Cérou, Arnaud Guyader.

This is a collaboration with Bernard Delyon (université de Rennes 1) and Mathias Rousset (EPI MATHERIALS, Inria Paris Rocquencourt).

By considering the adaptive multilevel splitting algorithm as a Fleming–Viot particle system for a stochastic wave, in the sense of  [42] , we have shown the mean square convergence using a general result  [67] about the convergence of Fleming–Viot (Villemonais, 2013). We are currently working on the proof of a central limit theorem, but the proof is not yet complete. We have nevertheless identified the expression of the asymptotic variance.