Particle in interactions: first steps to a theorem of convergence for the selection by stratification

Ivan Gentil (1) , Bruno Rémillard (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MQG - Méthodes Quantitatives de Gestion

This article focuses on the selection by stratification used on interacting particle systems. Interacting particle methods are used to approach particular probability measure. The selection by stratification is interesting because it the faster selection but unfortunately there is not convergence's theorem. We explain on this paper some properties, and the first steps to prove the convergence of the interacting particle systems to the probability measure.

Mots clés: Stationary Markov chains; Interacting particle systems; genetic algorithms; selection by stratification; Stationary Markov chains.

Domaines: Probabilités [math.PR]

Ivan Gentil, Bruno Rémillard. Particle in interactions: first steps to a theorem of convergence for the selection by stratification. Advances in Applied Probability, 2008, 40, pp.454-572. ⟨hal-00019334v3⟩