On the stability of measure valued processes with applications to filtering.

*(English. Abridged French version)*Zbl 0935.92001Summary: The purpose of this work is to present a novel approach to study the asymptotic stability of a class of measure valued processes arising in biology, in the theory of genetic type algorithms and in advanced signal processing. A new aspect of this result, as compared to existing literature on filtering, is that our approach is not based on auxiliary Hilbert projective metrics but only on Dobrushin’s ergodic coefficient. Another advantage is that it allows to treat time inhomogeneous signals taking values in a Polish space and it is not restricted to nonlinear filtering settings. What also makes our results interesting and new is that these qualitative properties lead to our knownledge to a first uniform convergence result with respect to time for a class of interacting particle schemes.