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Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

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\rightarrow0 and of (α,β) for Δ\rightarrow0 and ε\rightarrow0. 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.