Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps
The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/420648 |
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| _version_ | 1832556163876519936 |
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| author | Zhenyu Lu Tingya Yang Yanhan Hu Junhao Hu |
| author_facet | Zhenyu Lu Tingya Yang Yanhan Hu Junhao Hu |
| author_sort | Zhenyu Lu |
| collection | DOAJ |
| description | The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2. |
| format | Article |
| id | doaj-art-dc36eadf41554d2496ad644d49c24142 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dc36eadf41554d2496ad644d49c241422025-02-03T05:46:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/420648420648Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and JumpsZhenyu Lu0Tingya Yang1Yanhan Hu2Junhao Hu3College of Electrical and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, ChinaJiangsu Meteorological Observatory, Nanjing 210008, ChinaCollege of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, ChinaCollege of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, ChinaThe sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.http://dx.doi.org/10.1155/2013/420648 |
| spellingShingle | Zhenyu Lu Tingya Yang Yanhan Hu Junhao Hu Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps Abstract and Applied Analysis |
| title | Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps |
| title_full | Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps |
| title_fullStr | Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps |
| title_full_unstemmed | Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps |
| title_short | Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps |
| title_sort | convergence rate of numerical solutions for nonlinear stochastic pantograph equations with markovian switching and jumps |
| url | http://dx.doi.org/10.1155/2013/420648 |
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