Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation
The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense. Almost sure convergence is derived from the Lp convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is...
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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/10.1155/2014/390418 |
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| _version_ | 1832551271116046336 |
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| author | Qian Guo Xueyin Tao |
| author_facet | Qian Guo Xueyin Tao |
| author_sort | Qian Guo |
| collection | DOAJ |
| description | The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense. Almost sure convergence is derived from the Lp convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained. |
| format | Article |
| id | doaj-art-a84f8fa7e77142b79cc32d4319465e12 |
| 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-a84f8fa7e77142b79cc32d4319465e122025-02-03T06:01:55ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/390418390418Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential EquationQian Guo0Xueyin Tao1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaThe convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense. Almost sure convergence is derived from the Lp convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.http://dx.doi.org/10.1155/2014/390418 |
| spellingShingle | Qian Guo Xueyin Tao Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation Abstract and Applied Analysis |
| title | Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation |
| title_full | Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation |
| title_fullStr | Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation |
| title_full_unstemmed | Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation |
| title_short | Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation |
| title_sort | almost sure and lp convergence of split step backward euler method for stochastic delay differential equation |
| url | http://dx.doi.org/10.1155/2014/390418 |
| work_keys_str_mv | AT qianguo almostsureandlpconvergenceofsplitstepbackwardeulermethodforstochasticdelaydifferentialequation AT xueyintao almostsureandlpconvergenceofsplitstepbackwardeulermethodforstochasticdelaydifferentialequation |