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Zbl 0646.93057
Picard, Jean
Asymptotic study of estimation problems with small observation noise. (English)
[A] Stochastic modelling and filtering, Proc. IFIP-WG 7/1 Work. Conf., Rome/Italy 1984, Lect. Notes Control Inf. Sci. 91, 131-146 (1987).

[For the entire collection see Zbl 0624.00023.] \par The author discusses the standard nonlinear filtering problem when a `small amount' of noise is present in the observation process. This `small amount' is modelled by $\epsilon B\sb t$, where B is a standard Brownian motion and $\epsilon$ a positive parameter. Approximate finite dimensional filters are discussed and their asymptotic behaviour as $\epsilon\to 0$ is described.
[R.Elliott]

MSC 2000:: *93E11 Filtering in stochastic control
34E15 Asymptotic singular perturbations, general theory (ODE)
60H10 Stochastic ordinary differential equations

Keywords: nonlinear filtering; approximate finite dimensional filters

Citations: Zbl 0624.00023

Cited in: Zbl 0924.93044

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