An infinite expansion for nonlinear filtering
type: Item
instance of: scholarly article
title: An infinite expansion for nonlinear filtering
zbMATH Open document ID: 0810.62086
DOI: 10.1016/0304-4149(94)90049-3
author: Rui J. P. de Figueiredo
author: Yu Yaoqi
published in: Stochastic Processes and their Applications
publication date: 1994-11-08T00:00:00Z
review text: A filtering equation is obtained for a partially observed system in terms of the innovation process. This equation was obtained by \textit{Th. Kailath} and others in a different way under different conditions [see IEEE Trans. Automatic Control AC-13, No. 6, 646-660 (1968); AC-16, No. 6, 720-727 (1971); AC-18, No. 5, 435-453 (1973; Zbl 0263.93048); AC-18, No. 6, 588-607 (1973)]. An infinite series expansion of nonlinear filters as sums of multiple stochastic Itô integrals with respect to the innovation process is obtained. This expansion is used to calculate the conditional expectation as well as the innovation process.
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 672054
zbMATH Keywords: sums of multiple stochastic Ito integrals
zbMATH Keywords: predictable process
zbMATH Keywords: semimartingale
zbMATH Keywords: Ito formula
zbMATH Keywords: filtering equation
zbMATH Keywords: partially observed system
zbMATH Keywords: infinite series expansion of nonlinear filters
zbMATH Keywords: conditional expectation
zbMATH Keywords: innovation process
reviewed by: M. P. Moklyachuk
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90049-3
OpenAlex ID: W1979073422
cites work: Q3217388
cites work: Q3969647
cites work: Q4042404
cites work: Q4148534
cites work: Q3843987
cites work: Multiple Integral Expansions for Nonlinear Filtering
cites work: Q3321154
cites work: Convergence of the calculation of the innovation process
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description: scientific article; zbMATH DE number 672054