Small-diffusion asymptotics for discretely sampled stochastic differential equations

Abstract

1051-1069: The minimum-contrast estimation of drift and diffusion coefficient parameters for a multi-dimensional diffusion process with a small dispersion parameter $\varepsilon$ based on a Gaussian approximation to transition density is presented when the sample path is observed at equidistant times $k/n$, $k=0,1,\rm \dots,n$. We study asymptotic results for the minimum-contrast estimator as $\varepsilon$ goes to $0$ and $n$ goes to $\infty$ simultaneously.