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Stability of exact and numerical solutions for McKean–Vlasov stochastic differential equations with Hölder diffusion coefficients

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  • Liu, Zhuoqi
  • Gao, Shuaibin
  • Guo, Qian

Abstract

This paper investigates the long-time behavior of highly nonlinear McKean–Vlasov stochastic differential equations (MVSDEs) with Hölder continuous diffusion coefficients and their numerical approximations, which play an important role in the analysis of some real-world models. Based on the Yamada–Watanabe approximation technique, the primary goal is to prove that the exact solution tends to the equilibrium state in pth moment sense with p>0. Then, the propagation of chaos between the interacting particle system and non-interacting one is derived in the infinite horizon. To approximate such equations, a modified tamed Euler–Maruyama scheme is constructed for the corresponding interacting particle system, and its mean-square stability is rigorously demonstrated. We reveal that the numerical solution can reproduce the stability of the underlying MVSDE. The final part presents the numerical examples of long-time propagation of chaos and the mean-square stability of numerical solution, which are consistent with the theoretical results.

Suggested Citation

  • Liu, Zhuoqi & Gao, Shuaibin & Guo, Qian, 2026. "Stability of exact and numerical solutions for McKean–Vlasov stochastic differential equations with Hölder diffusion coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 746-760.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:746-760
    DOI: 10.1016/j.matcom.2026.02.031
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    References listed on IDEAS

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    1. Liu, Yicheng & Zhu, Quanxin, 2026. "Stability analysis of stochastic McKean–Vlasov equations with discrete observation," Applied Mathematics and Computation, Elsevier, vol. 511(C).
    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. Chen, Xingyuan & dos Reis, Gonçalo, 2022. "A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Jianhai Bao & Xing Huang, 2022. "Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1187-1215, June.
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