Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

2012/06/05 by Romain Guy, Guy, Romain, Catherine Larédo +3 · 1 citation
Computer Science · #62F12 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1206.0916

openalex publication_date 2012/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a multidimensional diffusion X with drift coefficient b(α,X(t)) and diffusion coefficient εσ(β,X(t)). The diffusion is discretely observed at times t_k=kΔ for k=1..n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ε. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ε→0 and of (α,β) for Δ→0 and ε→0. We compare the estimators obtained with various methods and for various magnitudes of Δ and ε based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.

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