# zbMATH — the first resource for mathematics

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 $$\epsilon B_ t$$, 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.
Reviewer: R.Elliott

##### MSC:
 93E11 Filtering in stochastic control theory 34E15 Singular perturbations, general theory for ordinary differential equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)