On the stability and the uniform propagation of chaos of Extended Ensemble Kalman-Bucy filters
Langue
en
Article de revue
Ce document a été publié dans
SIAM Journal on Control and Optimization. 2017, vol. 55, n° 1, p. 119-155
Society for Industrial and Applied Mathematics
Résumé en anglais
This article is concerned with the exponential stability and the uniform propagation of chaos properties of a class of Extended Ensemble Kalman-Bucy filters with respect to the time horizon. This class of nonlinear filters ...Lire la suite >
This article is concerned with the exponential stability and the uniform propagation of chaos properties of a class of Extended Ensemble Kalman-Bucy filters with respect to the time horizon. This class of nonlinear filters can be interpreted as the conditional expectations of nonlinear McKean Vlasov type diffusions with respect to the observation process. In contrast with more conventional Langevin nonlinear drift type processes, the mean field interaction is encapsulated in the covariance matrix of the diffusion. The main results discussed in the article are quantitative estimates of the exponential stability properties of these nonlinear diffusions. These stability properties are used to derive uniform and non asymptotic estimates of the propagation of chaos properties of Extended Ensemble Kalman filters, including exponential concentration inequalities. To our knowledge these results seem to be the first results of this type for this class of nonlinear ensemble type Kalman-Bucy filters.< Réduire
Mots clés en anglais
propagation of chaos properties
Ensemble Kalman filters
Extended Kalman-Bucy filter
mean field particle systems
stochastic Riccati matrix equation
uniform estimates
Monte Carlo methods
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