Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients
The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random me...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/675781 |
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| author | Hui Yu Minghui Song |
| author_facet | Hui Yu Minghui Song |
| author_sort | Hui Yu |
| collection | DOAJ |
| description | The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results. |
| format | Article |
| id | doaj-art-6ad68febab3a401987e5ad87ba024f1d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6ad68febab3a401987e5ad87ba024f1d2025-02-03T06:01:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/675781675781Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz CoefficientsHui Yu0Minghui Song1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThe numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results.http://dx.doi.org/10.1155/2012/675781 |
| spellingShingle | Hui Yu Minghui Song Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients Journal of Applied Mathematics |
| title | Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients |
| title_full | Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients |
| title_fullStr | Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients |
| title_full_unstemmed | Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients |
| title_short | Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients |
| title_sort | numerical solutions of stochastic differential equations driven by poisson random measure with non lipschitz coefficients |
| url | http://dx.doi.org/10.1155/2012/675781 |
| work_keys_str_mv | AT huiyu numericalsolutionsofstochasticdifferentialequationsdrivenbypoissonrandommeasurewithnonlipschitzcoefficients AT minghuisong numericalsolutionsofstochasticdifferentialequationsdrivenbypoissonrandommeasurewithnonlipschitzcoefficients |