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 ϵ σ ( β , X t ) . The diffusion sample path is discretely observed at times t k = k Δ 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.