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On a role of predictor in filtering stability

Le : 16/10/2006 11h00
Par : P. Chigansky (Université du Maine)
Lieu :
Lien web :
Résumé : The problem of filtering is to calculate the conditional distribution of the current state of the signal process, given the history of its noisy observations. For Markov processes, the conditional distribution satisfies a recursive filtering equation. The stability of this equation with respect to its initial condition is known under certain restrictive assumptions: typically the signal is required to be ergodic and to evolve on a compact state space. In this talk I will discuss certain predicting estimates of the signal state, which turn to be stable in a surprisingly general setting. The proof uses a change of measure and the martingale convergence and, unlike all other known methods, avoids direct analysis of the filtering equation.