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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-5
March 2002

Small diffusion asymptotics for discretely sampled stochastic differential equations


Michael Sørensen

Masayuki Uchida


The minimum contrast estimation of drift and diffusion coefficient parameters for a multi-dimensional diffusion process with a small dispersion parameter based on a Gaussian approximation to the transition density is presented in the situation where the sample path is observed at equidistant time points k/n, k=0,1, ... ,n. We study asymptotic results for the minimum contrast estimator as the dispersion parameter goes to zero and n goes to infinity simultaneously.

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This paper has now been published in Bernoulli, 9, 2003, 1051–1069