Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient
Résumé
We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ǫσ(β,Xt). The diffusion sample path is discretely observed at times tk = k for k = 1..n on a fixed interval [0, T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ǫ. We obtain consistent and asymptotically normal estimators of α for fixed and ǫ → 0 and of (α, β) for → 0 and ǫ → 0 without any condition linking ǫ and . We compare the estimators obtained with various methods and for various magnitudes of and ǫ based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.