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Titolo:
A Bayes formula for Gaussian noise processes and its applications
Autore:
Mandal, PK; Mandrekar, V;
Indirizzi:
EURANDOM, LG 1 21, NL-5600 MB Eindhoven, Netherlands EURANDOM Eindhoven Netherlands NL-5600 MB 5600 MB Eindhoven, Netherlands Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA Michigan State Univ E Lansing MI USA 48824 babil, E Lansing, MI 48824 USA
Titolo Testata:
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
fascicolo: 3, volume: 39, anno: 2000,
pagine: 852 - 871
SICI:
0363-0129(20001023)39:3<852:ABFFGN>2.0.ZU;2-#
Fonte:
ISI
Lingua:
ENG
Soggetto:
SIMPLE LINEAR-SYSTEM;
Keywords:
filtering; Gaussian noise process; Bayes formula; Ornstein-Uhlenbeck dispersion process; Zakai equation; fractional Brownian motion;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Engineering, Computing & Technology
Citazioni:
20
Recensione:
Indirizzi per estratti:
Indirizzo: Mandal, PK EURANDOM, LG 1 21, POB 513, NL-5600 MB Eindhoven, Netherlands EURANDOM POB 513 Eindhoven Netherlands NL-5600 MB Netherlands
Citazione:
P.K. Mandal e V. Mandrekar, "A Bayes formula for Gaussian noise processes and its applications", SIAM J CON, 39(3), 2000, pp. 852-871

Abstract

An elementary approach is used to derive a Bayes-type formula, extending the Kallianpur-Striebel formula for the nonlinear filters associated with the Gaussian noise processes. In the particular cases of certain Gaussian processes, recent results of Kunita and of Le Breton on fractional Brownian motion are derived. We also use the classical approximation of the Brownian motion by the Ornstein-Uhlenbeck dispersion process to solve the "instrumentability" problem of Balakrishnan. We give precise conditions for the convergence of the filter based on the Ornstein-Uhlenbeck dispersion process to the filter based on the Brownian motion. It is also shown that the solution of the Zakai equation can be approximated by that of a ( deterministic) partial differential equation.

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Documento generato il 01/12/20 alle ore 01:11:30