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 proble m involving convolutional integrals in its dynami...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Dynamic Publishers, Inc.
2010
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/12540/1/WP03.pdf |
| _version_ | 1803626438345097216 |
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| author | Misiran, Masnita Wu, Changzi Lu, Zudi Teo, K. L. |
| author_facet | Misiran, Masnita Wu, Changzi Lu, Zudi Teo, K. L. |
| author_sort | Misiran, Masnita |
| collection | UUM |
| description | 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 proble
m 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. |
| first_indexed | 2024-07-04T05:50:10Z |
| format | Article |
| id | uum-12540 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:50:10Z |
| publishDate | 2010 |
| publisher | Dynamic Publishers, Inc. |
| record_format | dspace |
| spelling | uum-125402014-11-05T00:43:50Z https://repo.uum.edu.my/id/eprint/12540/ Optimal filtering of linear system driven by fractional brownian motion Misiran, Masnita Wu, Changzi Lu, Zudi Teo, K. L. QA Mathematics 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 proble m 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. Dynamic Publishers, Inc. 2010-03-09 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/12540/1/WP03.pdf Misiran, Masnita and Wu, Changzi and Lu, Zudi and Teo, K. L. (2010) Optimal filtering of linear system driven by fractional brownian motion. Dynamic Systems an Applications, 19 (2010). pp. 495-514. ISSN 1056-2176 http://www.dynamicpublishers.org/journals/index.php/DSA/index |
| spellingShingle | QA Mathematics Misiran, Masnita Wu, Changzi Lu, Zudi Teo, K. L. Optimal filtering of linear system driven by fractional brownian motion |
| title | Optimal filtering of linear system driven by fractional brownian motion |
| title_full | Optimal filtering of linear system driven by fractional brownian motion |
| title_fullStr | Optimal filtering of linear system driven by fractional brownian motion |
| title_full_unstemmed | Optimal filtering of linear system driven by fractional brownian motion |
| title_short | Optimal filtering of linear system driven by fractional brownian motion |
| title_sort | optimal filtering of linear system driven by fractional brownian motion |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/12540/1/WP03.pdf |
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