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Optimal Filtering of Linear System Driven by Fractional Brownian Motion

Optimal Filtering of Linear System Driven by Fractional Brownian Motion
Optimal Filtering of Linear System Driven by Fractional Brownian Motion
In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness.
495-514
Misiran, Masnita
d00bf591-6648-43e9-819a-bb8f97465d09
Wu, Changzi
87af4407-bca0-45ea-a049-3d9f26bcadd8
Lu, Zudi
4aa7d988-ac2b-4150-a586-ca92b8adda95
Teo, K.L.
e559ebab-51d3-4fe8-8eab-db1206c55651
Misiran, Masnita
d00bf591-6648-43e9-819a-bb8f97465d09
Wu, Changzi
87af4407-bca0-45ea-a049-3d9f26bcadd8
Lu, Zudi
4aa7d988-ac2b-4150-a586-ca92b8adda95
Teo, K.L.
e559ebab-51d3-4fe8-8eab-db1206c55651

Misiran, Masnita, Wu, Changzi, Lu, Zudi and Teo, K.L. (2010) Optimal Filtering of Linear System Driven by Fractional Brownian Motion. Dynamic Systems and Applications, 19, 495-514.

Record type: Article

Abstract

In this paper, we consider a continuous time filtering of a multi-dimensional Langevin stochastic differential system driven by a fractional Brownian motion process. It is shown that this filtering problem is equivalent to an optimal control problem involving convolutional integrals in its dynamical system. Then, a novel approximation scheme is developed and applied to this optimal control problem. It yields a sequence of standard optimal control problems. The convergence of the approximate standard optimal control problem to the optimal control problem involving convolutional integrals in its system dynamics is established. Two numerical examples are solved by using the method proposed. The results obtained clearly demonstrate its efficiency and effectiveness.

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More information

Published date: 2010
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 360479
URI: http://eprints.soton.ac.uk/id/eprint/360479
PURE UUID: e97c394c-7210-42f2-9dfe-208539b88489
ORCID for Zudi Lu: ORCID iD orcid.org/0000-0003-0893-832X

Catalogue record

Date deposited: 10 Dec 2013 15:27
Last modified: 09 Jan 2022 03:46

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Contributors

Author: Masnita Misiran
Author: Changzi Wu
Author: Zudi Lu ORCID iD
Author: K.L. Teo

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