The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method
Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional sto...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/3805042 |
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| _version_ | 1832559371313217536 |
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| author | Yousef Alnafisah |
| author_facet | Yousef Alnafisah |
| author_sort | Yousef Alnafisah |
| collection | DOAJ |
| description | Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE. |
| format | Article |
| id | doaj-art-c44c9c0dee9a4524a3841cad6303e6e0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c44c9c0dee9a4524a3841cad6303e6e02025-02-03T01:30:14ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/38050423805042The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier MethodYousef Alnafisah0Mathematics Department, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaMultiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.http://dx.doi.org/10.1155/2018/3805042 |
| spellingShingle | Yousef Alnafisah The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method Abstract and Applied Analysis |
| title | The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method |
| title_full | The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method |
| title_fullStr | The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method |
| title_full_unstemmed | The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method |
| title_short | The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method |
| title_sort | implementation of milstein scheme in two dimensional sdes using the fourier method |
| url | http://dx.doi.org/10.1155/2018/3805042 |
| work_keys_str_mv | AT yousefalnafisah theimplementationofmilsteinschemeintwodimensionalsdesusingthefouriermethod AT yousefalnafisah implementationofmilsteinschemeintwodimensionalsdesusingthefouriermethod |