Convergence of a non-failable mean-field particle system

William Oçafrain 1 Denis Villemonais 2, 1, 3
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : The existing literature contains many examples of mean-field particle systems converging to the distribution of a Markov process conditioned to not hit a given set. In many situations, these mean-field particle systems are failable, meaning that they are not well defined after a given random time. Our first aim is to introduce an original mean-field particle system, which is always well defined and whose large number particle limit is, in all generality, the distribution of a process conditioned to not hit a given set. Under natural conditions on the underlying process, we also prove that the convergence holds uniformly in time as the number of particles goes to infinity. As an illustration, we show that our assumptions are satisfied in the case of a piece-wise deterministic Markov process.
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William Oçafrain, Denis Villemonais. Convergence of a non-failable mean-field particle system. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2017, 35 (4), pp.Pages 587-603. ⟨http://www.tandfonline.com/doi/full/10.1080/07362994.2017.1288136⟩. ⟨10.1080/07362994.2017.1288136⟩. ⟨hal-01338421⟩

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