Small-diffusion asymptotics for discretely sampled stochastic differential equations

Abstract

The minimum-contrast estimation of drift and diffusion coefficient parameters for a multidimensional diffusion process with a small dispersion parameter ε based on a Gaussian approximation to the transition density is presented when the sample path is observed at equidistant times k/n, k = 0, 1,..., n. We study asymptotic results for the minimum-contrast estimator as ε goes to 0 and n goes to ∞ simultaneously. © 2003 ISI/BS.