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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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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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References

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Feng Jiang

  2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Feng Jiang

  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

    Yi Shen & Xiaoxin Liao

Authors
  1. Feng Jiang
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  2. Yi Shen
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  3. Xiaoxin Liao
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Corresponding author

Correspondence to Feng Jiang.

Additional information

The work was supported by the Fundamental Research Funds for the Central Universities under Grant No. 2012089: 31541111213, China Postdoctoral Science Foundation Funded Project under Grant No. 2012M511615, and the State Key Program of National Natural Science of China under Grant No. 61134012.

This paper was recommended for publication by Editor Jinhu L Ü.

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Jiang, F., Shen, Y. & Liao, X. A note on stability of the split-step backward Euler method for linear stochastic delay integro-differential equations. J Syst Sci Complex 25, 873–879 (2012). https://doi.org/10.1007/s11424-012-0052-2

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  • DOI: https://doi.org/10.1007/s11424-012-0052-2

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