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On the convergence rate of approximation for distribution-dependent stochastic differential equations with Hölder continuous drift

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  • Wang, Lixi
  • Li, Junping

Abstract

In this work, we establish a new convergence result for Euler-Maruyama approximation to distribution-dependent stochastic differential equations with α-Hölder continuous drift, where α∈(0,1]. By innovatively combining the stochastic sewing technique and stochastic particle system method, we get a rate of convergence regarding the temporal step size (1/n) and the number of particles (N). Our analysis reveals distinct convergence behaviors under different noise structures: (i) For the general case of multiplicative noise, we obtain a rate with respect to the temporal step size that is arbitrarily close to the rate 1/2. A key advantage over existing literature is that our result is independent of the Hölder exponent α, which ensures robust convergence even for drifts with low regularity. (ii) For the special case of additive noise, we show that the convergence rate can be improved to arbitrarily close to 1/2+α/2.

Suggested Citation

  • Wang, Lixi & Li, Junping, 2026. "On the convergence rate of approximation for distribution-dependent stochastic differential equations with Hölder continuous drift," Applied Mathematics and Computation, Elsevier, vol. 513(C).
    • Handle: RePEc:eee:apmaco:v:513:y:2026:i:c:s0096300325005363
    DOI: 10.1016/j.amc.2025.129811
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    References listed on IDEAS

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    1. Menoukeu Pamen, Olivier & Taguchi, Dai, 2017. "Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2542-2559.
    2. De Angelis, Tiziano & Germain, Maximilien & Issoglio, Elena, 2022. "A numerical scheme for stochastic differential equations with distributional drift," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 55-90.
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