Some recent developments in nonlinear filtering theory
type: Item
instance of: scholarly article
title: Some recent developments in nonlinear filtering theory
zbMATH Open document ID: 0533.60049
DOI: 10.1007/BF00120483
author: Gopinath Kallianpur
author: Rajeeva L. Karandikar
published in: Acta Applicandae Mathematicae
publication date: 1983-01-01T00:00:00Z
review text: From two different points of view the authors review recent results in nonlinear filtering theory. The first part describes the use of (Itô-) stochastic calculus in estimating the state of a system from some observations, where the noise in both the signal and the observations is modeled by a Wiener process. Thus the authors derive the stochastic differential equation and the stochastic partial differential equation for the optimal filter. The second part is devoted to the finitely additive white noise model in filtering theory introduced by Balakrishnan. For this seemingly more practical and applicable model the analogous results are derived and compared to the filter equations for the Wiener model in part one. This comparison reveals a deep insight into connections between the recent attempts of making the Wiener-noise filtering model more instrumentable (Davis' robust solutions, Pardoux's solutions to s.p.d.e. etc.) and the finitely additive noise model.
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60A05
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 3846578
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: finitely additive white noise
zbMATH Keywords: robust filtering
reviewed by: Michael Kohlmann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00120483
OpenAlex ID: W4247261937
description: scientific article; zbMATH DE number 3846578