Averaging Principle for McKean-Vlasov SDEs Driven by FBMs

• Tongqi Zhang ^[1] ; Yong Xu ^[1] ; Lifang Feng ^[1] ; Bin Pei ^[1]
  1. [1] Northwestern Polytechnical University

     Northwestern Polytechnical University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper considers a class of mixed slow-fast McKean–Vlasov stochastic differential equations that contain the fractional Brownian motion with Hurst parameter H > 1/2 and the standard Brownian motion. Firstly, we prove an existence and uniqueness theorem for the mixed coupled system. Secondly, under suitable assumptions on the coefficients, using the approach of Khasminskii’s time discretization, we prove that the slow component strongly converges to the solution of the corresponding averaged equation in the mean square sense.

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