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Article Dans Une Revue Electronic Journal of Statistics Année : 2021

PARAMETRIC INFERENCE FOR SMALL VARIANCE AND LONG TIME HORIZON MCKEAN-VLASOV DIFFUSION MODELS

Résumé

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 t ≥ 0 and ε are derived. We then build an explicit approximate log-likelihood leading to consistent and asymptotically Gaussian estimators with original rates of convergence: the rate for the estimation of α is either ε −1 or √ T ε −1 , the rate for the estimation of β is √ T .
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Dates et versions

hal-03095560 , version 1 (04-01-2021)

Identifiants

Citer

Valentine Genon-Catalot, C. Laredo. PARAMETRIC INFERENCE FOR SMALL VARIANCE AND LONG TIME HORIZON MCKEAN-VLASOV DIFFUSION MODELS. Electronic Journal of Statistics , 2021, 15 (2), pp.5811-5854. ⟨10.1214/21-EJS1922⟩. ⟨hal-03095560⟩
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