Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ϵσ(β,Xt). The diffusion sample path is discretely observed at times tk=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 without any condition linking ϵ and Δ. 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.