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Mckean–Vlasov stochastic functional differential equations with common noise driven by fractional Brownian motions

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  • Wang, Jiangpeng
  • Shen, Guangjun
  • Zhang, Xuekang

Abstract

In this paper, we investigate Mckean–Vlasov stochastic functional differential equations with common noise driven by fractional Brownian motion with Hurst parameter H>12, where the dynamics of the underlying process depend on both its historical trajectories and the conditional probability distributions of the system. Firstly, by using the Carathéodory approximation method, we establish the well-posedness of solutions to the considered equations under non-Lipschitz conditions, and further analyze the continuity of the solutions with respect to the initial value. Secondly, we derive the conditional propagation of chaos property for the proposed equation framework, rigorously characterizing the asymptotic behavior of interacting particle systems. Our equation is a generalization of the model introduced by Carmona and Delarue (2018). Finally, a numerical example is presented to illustrate the validity of our theoretical results.

Suggested Citation

  • Wang, Jiangpeng & Shen, Guangjun & Zhang, Xuekang, 2026. "Mckean–Vlasov stochastic functional differential equations with common noise driven by fractional Brownian motions," Chaos, Solitons & Fractals, Elsevier, vol. 209(P1).
    • Handle: RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926006302
    DOI: 10.1016/j.chaos.2026.118489
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