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

Picard, Jean

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)

Keywords:

nonlinear filtering; approximate finite dimensional filters