A direct approach to deriving filtering equations for diffusion processes
type: Item
instance of: scholarly article
title: A direct approach to deriving filtering equations for diffusion processes
zbMATH Open document ID: 0974.60021
published in: Applied Mathematics and Optimization
publication date: 2001-12-16T00:00:00Z
full work available at URL: http://purl.umn.edu/3455
review text: The author gives a derivation of the so-called filtering equation for partially observable diffusion processes on the basis of the \(L_p\)-theory of SPDEs, without using any facts from filtering theory itself. The method of derivation is new and does not require any knowledge of filtering theory. After an introduction given in Section 1, Section 2 contains the statement of the problem and the main result (Theorem 2.10). In Section 3 the main idea of proving Theorem 2.10 is explained, and Section 4 contains necessary facts from the \(L_p\)-theory of SPDEs. The final Section 5 contains the proof of Theorem 2.10.
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 62M20
zbMATH DE Number: 1562974
zbMATH Keywords: filtering equation
zbMATH Keywords: partially observable diffusion processes
zbMATH Keywords: \(L_p\)-theory of stochastic partial differential equations
author: N. V. Krylov
author: Aleksandar Zatezalo
reviewed by: Gabriel V. Orman
MaRDI profile type: Publication
OpenAlex ID: W1998254003
DOI: 10.1007/S002450010015
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description: scientific article; zbMATH DE number 1562974