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A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations |
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| Authors: | Feng Jiang Yi Shen Xiaoxin Liao |
| Affiliation: | 1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China 2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China 3. Department of Control Science and Engineering, the Key Laboratory of Ministry of Eduction for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, China |
| Abstract: | In the literature (Tan and Wang, 2010), Tan and Wang investigated the convergence of the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the mean-square stability of SSBE method under some condition. Unfortunately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory. |
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