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October 20, 2025Open Access

Asymptotic behaviors of multiscale McKean-Vlasov stochastic systems

Key Points

The slow component converges to the solution of the averaging equation in the Lp space with optimal order 1/2.
A central limit theorem establishes weak convergence rates, revealing dynamics in multiscale stochastic systems.
The Poisson equation method is applied effectively to derive key results in the behavior of these systems.
These findings could have implications in understanding complex interactions in stochastic modeling.

Abstract

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove that the slow component converges to the solution of the averaging equation in the Lᵖ (p 2) space with the optimal convergence order 12. Then we establish a central limit theorem for these systems and derive the weak convergence rate using the Poisson equation technique and the regularity properties of the associated Cauchy problem.

Asymptotic behaviors of multiscale McKean-Vlasov stochastic systems

Key Points

Abstract

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