On the stability and the uniform propagation of chaos of Extended Ensemble Kalman-Bucy filters

Pierre del Moral (1) , Aline Kurtzmann (2) , Julian Tugaut (3)

1 CQFD - Quality control and dynamic reliability
2 IECL - Institut Élie Cartan de Lorraine
3 PSPM - Probabilités, statistique, physique mathématique

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.

Mots clés: propagation of chaos properties; Ensemble Kalman filters; Extended Kalman-Bucy filter; mean field particle systems; stochastic Riccati matrix equation; uniform estimates; Monte Carlo methods

Domaines: Probabilités [math.PR]

Pierre del Moral, Aline Kurtzmann, Julian Tugaut. On the stability and the uniform propagation of chaos of Extended Ensemble Kalman-Bucy filters. SIAM Journal on Control and Optimization, 2017, 55 (1), pp.119-155. ⟨10.1137/16M1087497⟩. ⟨hal-01337716⟩