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Averaging principle for the fast–slow McKean–Vlasov stochastic differential equations driven by mixed fractional Brownian motion

Part of: Equations and systems with randomness Stochastic analysis

Published online by Cambridge University Press:  05 June 2025

Yaru Jiang  and
Meiling Zhao
Yaru Jiang*
Affiliation:
Anhui Jianzhu University
Meiling Zhao*
Affiliation:
Anhui Jianzhu University
*
*Postal address: School of Mathematics and Physics, Anhui Jianzhu University, Hefei, Anhui, 230601, PR China.
*Postal address: School of Mathematics and Physics, Anhui Jianzhu University, Hefei, Anhui, 230601, PR China.
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Abstract

This paper focuses on the averaging principle concerning the fast–slow McKean–Vlasov stochastic differential equations driven by mixed fractional Brownian motion with Hurst parameter $\tfrac{1}{2} < H < 1$. The integral associated with Brownian motion is the standard Itô integral, while the integral with respect to fractional Brownian motion is a generalized Riemann–Stieltjes integral. Under the non-Lipschitz condition and certain appropriate assumptions regarding the coefficients, we initially establish the existence and uniqueness theorem for the fast–slow McKean–Vlasov stochastic differential equation driven by mixed fractional Brownian motion. Subsequently, we demonstrate the averaging principle of the fast–slow McKean–Vlasov stochastic differential equations, signifying that the slow stochastic differential equation converges to the associated averaged equation in terms of mean-square convergence.

Keywords

Averaging principleMcKean–Vlasov stochastic differential equationfractional Brownian motionnon-Lipschitz condition

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 34F05: Equations and systems with randomness
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 20
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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