Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps
To realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximatio...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/159107 |
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| _version_ | 1832548630624468992 |
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| author | Ying Du Changlin Mei |
| author_facet | Ying Du Changlin Mei |
| author_sort | Ying Du |
| collection | DOAJ |
| description | To realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximations in solving stochastic differential equations, we propose two implicit methods, the θ-Taylor method and the balanced θ-Taylor method, for numerically solving the stochastic differential equation with jumps and prove that the numerical solutions are convergent with strong order 1.0. For a linear scalar test equation, the mean-square stability regions of the methods are derived. Finally, numerical examples are given to evaluate the performance of the methods. |
| format | Article |
| id | doaj-art-b5c5287f6f6d4356b86f2843502aa4a5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b5c5287f6f6d4356b86f2843502aa4a52025-02-03T06:13:36ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/159107159107Implicit Numerical Solutions for Solving Stochastic Differential Equations with JumpsYing Du0Changlin Mei1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaTo realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximations in solving stochastic differential equations, we propose two implicit methods, the θ-Taylor method and the balanced θ-Taylor method, for numerically solving the stochastic differential equation with jumps and prove that the numerical solutions are convergent with strong order 1.0. For a linear scalar test equation, the mean-square stability regions of the methods are derived. Finally, numerical examples are given to evaluate the performance of the methods.http://dx.doi.org/10.1155/2014/159107 |
| spellingShingle | Ying Du Changlin Mei Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps Abstract and Applied Analysis |
| title | Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps |
| title_full | Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps |
| title_fullStr | Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps |
| title_full_unstemmed | Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps |
| title_short | Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps |
| title_sort | implicit numerical solutions for solving stochastic differential equations with jumps |
| url | http://dx.doi.org/10.1155/2014/159107 |
| work_keys_str_mv | AT yingdu implicitnumericalsolutionsforsolvingstochasticdifferentialequationswithjumps AT changlinmei implicitnumericalsolutionsforsolvingstochasticdifferentialequationswithjumps |