Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses
In this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition. By using the linear operator theory, we deal with the difficulty brought by delay term of the neutral system and obtain the conclusion that the so...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6731091 |
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| _version_ | 1832565990286688256 |
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| author | Peiguang Wang Yan Xu |
| author_facet | Peiguang Wang Yan Xu |
| author_sort | Peiguang Wang |
| collection | DOAJ |
| description | In this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition. By using the linear operator theory, we deal with the difficulty brought by delay term of the neutral system and obtain the conclusion that the solutions of neutral stochastic delay differential equations with impulses converge to the solutions of the corresponding averaged stochastic delay differential equations without impulses in the sense of mean square and in probability. At last, an example is presented to show the validity of the proposed theories. |
| format | Article |
| id | doaj-art-4b7c2ae4dbc241fa955b8b60dbf16f74 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-4b7c2ae4dbc241fa955b8b60dbf16f742025-02-03T01:05:22ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/67310916731091Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with ImpulsesPeiguang Wang0Yan Xu1College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, ChinaCollege of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, ChinaIn this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition. By using the linear operator theory, we deal with the difficulty brought by delay term of the neutral system and obtain the conclusion that the solutions of neutral stochastic delay differential equations with impulses converge to the solutions of the corresponding averaged stochastic delay differential equations without impulses in the sense of mean square and in probability. At last, an example is presented to show the validity of the proposed theories.http://dx.doi.org/10.1155/2020/6731091 |
| spellingShingle | Peiguang Wang Yan Xu Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses Complexity |
| title | Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses |
| title_full | Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses |
| title_fullStr | Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses |
| title_full_unstemmed | Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses |
| title_short | Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses |
| title_sort | periodic averaging principle for neutral stochastic delay differential equations with impulses |
| url | http://dx.doi.org/10.1155/2020/6731091 |
| work_keys_str_mv | AT peiguangwang periodicaveragingprincipleforneutralstochasticdelaydifferentialequationswithimpulses AT yanxu periodicaveragingprincipleforneutralstochasticdelaydifferentialequationswithimpulses |