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Non-confluence of fractional stochastic differential equations driven by Lévy process

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Abstract

In this paper, we investigate a class of stochastic Riemann-Liouville type fractional differential equations driven by Lévy noise. By using Itô formula for the considered equation, we attempt to explore the non-confluence property of solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions which is novel in exploring the non-confluence property of differential equations.

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Acknowledgements

The authors Zhi Li and Liping Xu are partially financial supported by the NNSF of China (No. 11901058) and Natural Science Foundation of Hubei Province (No. 2021CFB543). The author Tianquan Feng is partially financial supported by the NNSF of China (No. 61906095).

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Authors and Affiliations

  1. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, Hubei, People’s Republic of China

    Zhi Li & Liping Xu

  2. School of Medicine, Yangtze University, Jingzhou, 434023, Hubei, People’s Republic of China

    Tianquan Feng

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  1. Zhi Li
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  2. Tianquan Feng
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  3. Liping Xu
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Correspondence to Tianquan Feng.

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Li, Z., Feng, T. & Xu, L. Non-confluence of fractional stochastic differential equations driven by Lévy process. Fract Calc Appl Anal 27, 1414–1427 (2024). https://doi.org/10.1007/s13540-024-00278-0

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  • DOI: https://doi.org/10.1007/s13540-024-00278-0

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