February 2025 Maximum likelihood estimation for small noise multi-scale McKean-Vlasov stochastic differential equations
Jie Xu, Qiao Zheng, Jianyong Mu
Author Affiliations +
Bernoulli 31(1): 783-815 (February 2025). DOI: 10.3150/24-BEJ1750

Abstract

In this paper we focus on the problem of the parameter estimation for a class of systems described by multi-scale McKean-Vlasov stochastic differential equations (MVSDEs, for short) with small noise, where the coefficients depend on the slow component, the fast component, and their own distributions. Firstly, we prove an optimal strong convergence rate of the strong averaging principle of the slow process by using the technique of Poisson equation. Secondly, we construct the maximum likelihood estimator (MLE, for short) and prove its consistency and asymptotic normality. Finally, an example is presented to illustrate the theoretical findings.

Acknowledgements

The authors are very deeply grateful to the Editor-in-Chief, the Associate Editor, the anonymous reviewer and Professor Yu Miao for their careful reading of manuscript, correcting errors, detailed comments and valuable suggestions, which improve the quality of this paper. The first author also acknowledges the support provided by key scientific research project plans of Henan province advanced universities No. 24A110006. Jie Xu is the corresponding author.

Citation

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Jie Xu. Qiao Zheng. Jianyong Mu. "Maximum likelihood estimation for small noise multi-scale McKean-Vlasov stochastic differential equations." Bernoulli 31 (1) 783 - 815, February 2025. https://doi.org/10.3150/24-BEJ1750

Information

Received: 1 June 2023; Published: February 2025
First available in Project Euclid: 30 October 2024

Digital Object Identifier: 10.3150/24-BEJ1750

Keywords: McKean-Vlasov equation , multi-scale system , Parameter estimation , small noise

Vol.31 • No. 1 • February 2025
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