Convergence of a non-failable mean-field particle system. Issue 4 (4th July 2017)

• Record Type: Journal Article
• Authors: Oçafrain, William; Villemonais, Denis
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 4(2017)
• Page Start: 587
• Page End: 603
• Publication Date: 2017-07-04
• Subjects: Mean-field particle system -- process with absorption -- Monte-Carlo method -- quasi-stationary distribution; Primary: 37A25 -- 60B10 -- 60F99 -- Secondary: 60J80; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1288136
• Languages: English
• ISSNs: 0736-2994

Abstract

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.