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Convergence and stability of the split-step composite \(\theta \)-Milstein method for stochastic delay differential equations

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Abstract

This research analyzes split-step composite \(\theta \)-Milstein (SSCTM) method based on stochastic delay differential equations, with particular focuses on examining its convergence and stability. We prove SSCTM method converges with strong order 1. Sufficient conditions for stability are given. Further, the regions in which SSCTM method exhibits stability are investigated. Numerical simulations validate our theoretical part.

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Funding

This work was supported by the [National Natural Science Foundation of China] under Grant [Numbers 61763008, 71762008, 62166015]; and the [Guangxi Science and Technology Planning Project] under Grant [Numbers 2018GXNSFAA294131, 2018GXNSFAA050005].

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Authors and Affiliations

  1. School of Science, Guilin University of Technology, Guilin, 541006, Guangxi, China

    Yuanqiao Lu, Haomin Zhang & Songyu Hong

  2. Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin University of Technology, Guilin, 541000, Guangxi, China

    Haomin Zhang

Authors
  1. Yuanqiao Lu
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  2. Haomin Zhang
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  3. Songyu Hong
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Contributions

YL contributed to conceptualization, methodology, software, formal analysis, writing—original draft, and writing—review and editing; HZ contributed to validation, writing—review and editing, supervision, project administration, and funding acquisition; SH contributed to investigation and visualization.

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Correspondence to Haomin Zhang.

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Lu, Y., Zhang, H. & Hong, S. Convergence and stability of the split-step composite \(\theta \)-Milstein method for stochastic delay differential equations. Int. J. Dynam. Control 12, 1302–1313 (2024). https://doi.org/10.1007/s40435-023-01253-y

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  • DOI: https://doi.org/10.1007/s40435-023-01253-y

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