Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions
The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/127397 |
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| _version_ | 1832565243790753792 |
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| author | Minghui Song Hui Yu |
| author_facet | Minghui Song Hui Yu |
| author_sort | Minghui Song |
| collection | DOAJ |
| description | The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results. |
| format | Article |
| id | doaj-art-7b0e0f1fa4094c4c9896756c222f4f16 |
| 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-7b0e0f1fa4094c4c9896756c222f4f162025-02-03T01:08:57ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/127397127397Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type ConditionsMinghui Song0Hui Yu1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThe Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results.http://dx.doi.org/10.1155/2012/127397 |
| spellingShingle | Minghui Song Hui Yu Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions Abstract and Applied Analysis |
| title | Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions |
| title_full | Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions |
| title_fullStr | Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions |
| title_full_unstemmed | Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions |
| title_short | Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions |
| title_sort | numerical solutions of stochastic differential delay equations with poisson random measure under the generalized khasminskii type conditions |
| url | http://dx.doi.org/10.1155/2012/127397 |
| work_keys_str_mv | AT minghuisong numericalsolutionsofstochasticdifferentialdelayequationswithpoissonrandommeasureunderthegeneralizedkhasminskiitypeconditions AT huiyu numericalsolutionsofstochasticdifferentialdelayequationswithpoissonrandommeasureunderthegeneralizedkhasminskiitypeconditions |