Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments
The main purpose of this paper is to investigate the strong convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). Firstly, it is proved that the Euler approximation solution converges to the analytic solution under local Lipschitz conditio...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/643783 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849414424656347136 |
|---|---|
| author | Ling Zhang Minghui Song |
| author_facet | Ling Zhang Minghui Song |
| author_sort | Ling Zhang |
| collection | DOAJ |
| description | The main purpose of this paper is to investigate the strong convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). Firstly, it is proved that the Euler approximation solution converges to the analytic solution under local Lipschitz condition and the bounded pth moment condition. Secondly, the Euler approximation solution converge to the analytic solution is given under local Lipschitz condition and the linear growth condition. Then an example is provided to show which is satisfied with the monotone condition without the linear growth condition. Finally, the convergence of numerical solutions to SEPCAs under local Lipschitz condition and the monotone condition is established. |
| format | Article |
| id | doaj-art-73818e1d9dd3484b8e38cca166b48d09 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-73818e1d9dd3484b8e38cca166b48d092025-08-20T03:33:50ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/643783643783Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous ArgumentsLing Zhang0Minghui Song1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThe main purpose of this paper is to investigate the strong convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). Firstly, it is proved that the Euler approximation solution converges to the analytic solution under local Lipschitz condition and the bounded pth moment condition. Secondly, the Euler approximation solution converge to the analytic solution is given under local Lipschitz condition and the linear growth condition. Then an example is provided to show which is satisfied with the monotone condition without the linear growth condition. Finally, the convergence of numerical solutions to SEPCAs under local Lipschitz condition and the monotone condition is established.http://dx.doi.org/10.1155/2012/643783 |
| spellingShingle | Ling Zhang Minghui Song Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments Abstract and Applied Analysis |
| title | Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments |
| title_full | Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments |
| title_fullStr | Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments |
| title_full_unstemmed | Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments |
| title_short | Convergence of the Euler Method of Stochastic Differential Equations with Piecewise Continuous Arguments |
| title_sort | convergence of the euler method of stochastic differential equations with piecewise continuous arguments |
| url | http://dx.doi.org/10.1155/2012/643783 |
| work_keys_str_mv | AT lingzhang convergenceoftheeulermethodofstochasticdifferentialequationswithpiecewisecontinuousarguments AT minghuisong convergenceoftheeulermethodofstochasticdifferentialequationswithpiecewisecontinuousarguments |