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...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Dynamic Publishers
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/9384 |
| _version_ | 1848745933879115776 |
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| author | Misiran, Masnita Wu, C. Lu, Z. Teo, Kok Lay |
| author_facet | Misiran, Masnita Wu, C. Lu, Z. Teo, Kok Lay |
| author_sort | Misiran, Masnita |
| building | Curtin Institutional Repository |
| collection | Online Access |
| 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 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. |
| first_indexed | 2025-11-14T06:25:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-9384 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:25:14Z |
| publishDate | 2010 |
| publisher | Dynamic Publishers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-93842017-01-30T11:12:21Z Optimal Filtering of Linear System Driven by Fractional Brownian Motion Misiran, Masnita Wu, C. Lu, Z. Teo, Kok Lay fractional Brownian motion approximation scheme convolutional integrals optimal control approximate optimal control computation linear filtering 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. 2010 Journal Article http://hdl.handle.net/20.500.11937/9384 Dynamic Publishers fulltext |
| spellingShingle | fractional Brownian motion approximation scheme convolutional integrals optimal control approximate optimal control computation linear filtering Misiran, Masnita Wu, C. Lu, Z. Teo, Kok Lay 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 | fractional Brownian motion approximation scheme convolutional integrals optimal control approximate optimal control computation linear filtering |
| url | http://hdl.handle.net/20.500.11937/9384 |