Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients
The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exac...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/830936 |
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| _version_ | 1832560978321997824 |
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| author | Peng Jiang Xiaofeng Ju Dan Liu Shaoqun Fan |
| author_facet | Peng Jiang Xiaofeng Ju Dan Liu Shaoqun Fan |
| author_sort | Peng Jiang |
| collection | DOAJ |
| description | The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper. |
| format | Article |
| id | doaj-art-e74c404cb25d42cba5173b372396815e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e74c404cb25d42cba5173b372396815e2025-02-03T01:26:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/830936830936Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant CoefficientsPeng Jiang0Xiaofeng Ju1Dan Liu2Shaoqun Fan3Harbin Institute of Technology, Room 405, Apartment A11, 92 Xi Dazhi Street, Harbin, Heilongjiang 150001, ChinaSchool of Management, Harbin Institute of Technology, Room 225, 92 Xi Dazhi Street, Harbin, Heilongjiang 150001, ChinaQingdao Technical College, 369 Qiantangjiang Road, Qingdao Economic and Technological Development Zone, Qingdao, Shandong 266555, ChinaChina Telecom Beijing Research Institute, 708 Guanhua Building, No. 118 Xizhimennei Street, Xicheng District, Beijing 100035, ChinaThe authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.http://dx.doi.org/10.1155/2013/830936 |
| spellingShingle | Peng Jiang Xiaofeng Ju Dan Liu Shaoqun Fan Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients Journal of Applied Mathematics |
| title | Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients |
| title_full | Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients |
| title_fullStr | Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients |
| title_full_unstemmed | Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients |
| title_short | Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients |
| title_sort | exact finite difference schemes for d dimensional linear stochastic systems with constant coefficients |
| url | http://dx.doi.org/10.1155/2013/830936 |
| work_keys_str_mv | AT pengjiang exactfinitedifferenceschemesforddimensionallinearstochasticsystemswithconstantcoefficients AT xiaofengju exactfinitedifferenceschemesforddimensionallinearstochasticsystemswithconstantcoefficients AT danliu exactfinitedifferenceschemesforddimensionallinearstochasticsystemswithconstantcoefficients AT shaoqunfan exactfinitedifferenceschemesforddimensionallinearstochasticsystemswithconstantcoefficients |