IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v502y2025ics0096300325002048.html

Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions

Author

Listed:
  • Wang, Shengrong
  • Xie, Jie
  • Tan, Li

Abstract

The primary objective of this paper is to explore the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent H∈(1/2,1). After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama (EM) scheme and show that the numerical solution convergent to the true solution strongly. Furthermore, a related example is given to illustrate the theory.

Suggested Citation

  • Wang, Shengrong & Xie, Jie & Tan, Li, 2025. "Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions," Applied Mathematics and Computation, Elsevier, vol. 502(C).
    • Handle: RePEc:eee:apmaco:v:502:y:2025:i:c:s0096300325002048
    DOI: 10.1016/j.amc.2025.129478
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325002048
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129478?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    2. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    3. Fan, Xiliang & Huang, Xing & Suo, Yongqiang & Yuan, Chenggui, 2022. "Distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 23-67.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guangjun Shen & Qian Yu, 2026. "McKean–Vlasov Stochastic Differential Equations Driven by Fractional Stable Processes: Well-Posedness, Propagation of Chaos, Averaging Principle," Journal of Theoretical Probability, Springer, vol. 39(2), pages 1-28, June.
    2. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    3. Shen, Guangjun & Wang, Jiangpeng, 2025. "Conditional McKean–Vlasov stochastic differential equations driven by fractional Brownian motions," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    4. Li, Hanwu, 2024. "Backward stochastic differential equations with double mean reflections," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    5. Fu, Zongkui & Fei, Dandan, 2025. "General mean-field reflected backward stochastic differential equations with locally monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 216(C).
    6. Buckdahn, Rainer & Chen, Yajie & Li, Juan, 2021. "Partial derivative with respect to the measure and its application to general controlled mean-field systems," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 265-307.
    7. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    8. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    9. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.
    10. Wei Zhang & Hui Min, 2023. "$$L^p$$ L p -Error Estimates for Numerical Schemes for Solving Certain Kinds of Mean-Field Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(2), pages 762-778, June.
    11. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    12. Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.
    13. Li, Butong & Meng, Yongna & Sun, Xiaobin & Yang, Ting, 2022. "Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation," Statistics & Probability Letters, Elsevier, vol. 191(C).
    14. Ren, Panpan & Wu, Jiang-Lun, 2021. "Least squares estimation for path-distribution dependent stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    15. Alexander Kalinin & Thilo Meyer-Brandis & Frank Proske, 2024. "Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments," Journal of Theoretical Probability, Springer, vol. 37(4), pages 2941-2989, November.
    16. Roxana Dumitrescu & Bernt Øksendal & Agnès Sulem, 2018. "Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 559-584, March.
    17. Zhongmin Qian & Yuhan Yao, 2022. "McKean–Vlasov type stochastic differential equations arising from the random vortex method," Partial Differential Equations and Applications, Springer, vol. 3(1), pages 1-22, February.
    18. Ren, Panpan, 2023. "Singular McKean–Vlasov SDEs: Well-posedness, regularities and Wang’s Harnack inequality," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 291-311.
    19. Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    20. Xing Huang & Xiaochen Ma, 2024. "Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3152-3176, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:502:y:2025:i:c:s0096300325002048. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.