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Asymptotic study of estimation problems with small observation noise. (English) Zbl 0646.93057
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.]

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 $ϵ{B}_{t}$, where B is a standard Brownian motion and $ϵ$ a positive parameter. Approximate finite dimensional filters are discussed and their asymptotic behaviour as $ϵ\to 0$ is described.

Reviewer: R.Elliott

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