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2021 Parametric inference for small variance and long time horizon McKean-Vlasov diffusion models
Valentine Genon-Catalot, Catherine Larédo
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Electron. J. Statist. 15(2): 5811-5854 (2021). DOI: 10.1214/21-EJS1922

Abstract

Let (Xt) be solution of a one-dimensional McKean-Vlasov stochastic differential equation with classical drift term V(α,x), self-stabilizing term Φ(β,x) and small noise amplitude ε. Our aim is to study the estimation of the unknown parameters α,β from a continuous observation of (Xt,t[0,T]) under the double asymptotic framework ε tends to 0 and T tends to infinity. After centering and normalization of the process, uniform bounds for moments with respect to t0 and ε are derived. We then build an explicit approximate log-likelihood leading to consistent and asymptotically Gaussian estimators, under the condition that εT tends to 0, with original rates of convergence: the rate for the estimation of α is either ε1 or Tε1, the rate for the estimation of β is T. Moreover, the estimators are asymptotically efficient.

Acknowledgments

We thank the two referees for their helpful and detailed comments.

Citation

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Valentine Genon-Catalot. Catherine Larédo. "Parametric inference for small variance and long time horizon McKean-Vlasov diffusion models." Electron. J. Statist. 15 (2) 5811 - 5854, 2021. https://doi.org/10.1214/21-EJS1922

Information

Received: 1 January 2021; Published: 2021
First available in Project Euclid: 27 December 2021

Digital Object Identifier: 10.1214/21-EJS1922

Subjects:
Primary: 60J60 , 60J99 , 62F12 , 62M05

Keywords: Asymptotic properties of estimators , continuous observations , infinite time horizon , McKean-Vlasov stochastic differential equations , Parametric inference , small noise

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Vol.15 • No. 2 • 2021
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