P. Del Moral et A. Guionnet, On the stability of interacting processes with applications to filtering and genetic algorithms, ANN IHP-PR, 37(2), 2001, pp. 155-194
Citations number
37
Categorie Soggetti
Mathematics
Journal title
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
The stability properties of a class of interacting measure valued processes
arising in nonlinear filtering and genetic algorithm theory is discussed.
Simple sufficient conditions are given for exponential decays. These criter
ia are applied to study the asymptotic stability of the nonlinear filtering
equation and infinite population models as those arising in Biology and ev
olutionary computing literature.
On the basis of these stability properties we also propose a uniform conver
gence theorem for the interacting particle numerical scheme of the nonlinea
r filtering equation introduced in a previous work. In the last part of thi
s study we propose a refinement genetic type particle method with periodic
selection dates and we improve the previous uniform convergence results. We
finally discuss the uniform convergence of particle approximations includi
ng branching and random population size systems. (C) 2001 Editions scientif
iques et medicales Elsevier SAS.