Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations
Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the...
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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/10.1155/2014/751209 |
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| _version_ | 1832563752454586368 |
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| author | Shaobo Zhou |
| author_facet | Shaobo Zhou |
| author_sort | Shaobo Zhou |
| collection | DOAJ |
| description | Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the Euler-Maruyama (EM) method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. And the backward EM method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations. A highly nonlinear example is provided to illustrate the main theory. |
| format | Article |
| id | doaj-art-0c7109e25447493a98213250c6762b54 |
| 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-0c7109e25447493a98213250c6762b542025-02-03T01:12:34ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/751209751209Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph EquationsShaobo Zhou0School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaOur effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the Euler-Maruyama (EM) method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. And the backward EM method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations. A highly nonlinear example is provided to illustrate the main theory.http://dx.doi.org/10.1155/2014/751209 |
| spellingShingle | Shaobo Zhou Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations Abstract and Applied Analysis |
| title | Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations |
| title_full | Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations |
| title_fullStr | Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations |
| title_full_unstemmed | Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations |
| title_short | Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations |
| title_sort | almost surely exponential stability of numerical solutions for stochastic pantograph equations |
| url | http://dx.doi.org/10.1155/2014/751209 |
| work_keys_str_mv | AT shaobozhou almostsurelyexponentialstabilityofnumericalsolutionsforstochasticpantographequations |