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- W2007171567 abstract "We study the a.s. exponential stability of the optimal filter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the filter) for a general setting both in discrete and in continuous time, in terms of Birkhoff's contraction coefficient. Criteria for exponential stability and explicit bounds on the rate are given in the specific cases of a diffusion process on a compact manifold, and discrete time Markov chains on both continuous and discrete-countable state spaces. A similar question regarding the optimal smoother is investigated and a stability criterion is provided. Nous étudions la stabilité du filtre optimal par rapport à ses conditions initiales. Le taux de décroissance exponentielle est calculé dans un cadre général, pour temps discret et temps continu, en terme du coefficient de contraction de Birkhoff. Des critères de stabilité exponentielle et des bornes explicites sur le taux sont calculés pour les cas particuliers d'une diffusion sur une variété compacte, ainsi que pour des chaînes de Markov sur un espace discret ou continu." @default.
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- W2007171567 date "1997-01-01" @default.
- W2007171567 modified "2023-09-29" @default.
- W2007171567 title "Exponential stability for nonlinear filtering" @default.
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- W2007171567 doi "https://doi.org/10.1016/s0246-0203(97)80110-0" @default.
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