A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations
Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a...
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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: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/750147 |
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| _version_ | 1832562496851935232 |
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| author | Yanli Zhou Yonghong Wu Xiangyu Ge B. Wiwatanapataphee |
| author_facet | Yanli Zhou Yonghong Wu Xiangyu Ge B. Wiwatanapataphee |
| author_sort | Yanli Zhou |
| collection | DOAJ |
| description | Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations. |
| format | Article |
| id | doaj-art-b6e983c41c884ecdb2c6ea2040d90f0d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b6e983c41c884ecdb2c6ea2040d90f0d2025-02-03T01:22:33ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/750147750147A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential EquationsYanli Zhou0Yonghong Wu1Xiangyu Ge2B. Wiwatanapataphee3Department of Maths and Statistics, Curtin University, Perth, WA 6845, AustraliaDepartment of Maths and Statistics, Curtin University, Perth, WA 6845, AustraliaSchool of Statistics & Maths, Zhongnan University of Economics and Law, Wuhan 430073, ChinaDepartment of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandStochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations.http://dx.doi.org/10.1155/2013/750147 |
| spellingShingle | Yanli Zhou Yonghong Wu Xiangyu Ge B. Wiwatanapataphee A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations Abstract and Applied Analysis |
| title | A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations |
| title_full | A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations |
| title_fullStr | A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations |
| title_full_unstemmed | A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations |
| title_short | A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations |
| title_sort | robust weak taylor approximation scheme for solutions of jump diffusion stochastic delay differential equations |
| url | http://dx.doi.org/10.1155/2013/750147 |
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