This investigation shows the asymptotic behavior of maximum likelihood estimates in diffusion processes, suggesting consistency with classical results.
We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.
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Brown et al. (1975) studied this question.
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