  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.
