Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations
We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/217672 |
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| _version_ | 1832559467952078848 |
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| author | Zhanhua Yu Mingzhu Liu |
| author_facet | Zhanhua Yu Mingzhu Liu |
| author_sort | Zhanhua Yu |
| collection | DOAJ |
| description | We investigate the almost surely asymptotic stability of Euler-type
methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results. |
| format | Article |
| id | doaj-art-176ad2c555494d24b394c05a80b3507b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-176ad2c555494d24b394c05a80b3507b2025-02-03T01:29:56ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/217672217672Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential EquationsZhanhua Yu0Mingzhu Liu1Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.http://dx.doi.org/10.1155/2011/217672 |
| spellingShingle | Zhanhua Yu Mingzhu Liu Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations Discrete Dynamics in Nature and Society |
| title | Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations |
| title_full | Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations |
| title_fullStr | Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations |
| title_full_unstemmed | Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations |
| title_short | Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations |
| title_sort | almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations |
| url | http://dx.doi.org/10.1155/2011/217672 |
| work_keys_str_mv | AT zhanhuayu almostsurelyasymptoticstabilityofnumericalsolutionsforneutralstochasticdelaydifferentialequations AT mingzhuliu almostsurelyasymptoticstabilityofnumericalsolutionsforneutralstochasticdelaydifferentialequations |