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Estimators of diffusions with randomly spaced discrete observations: A general theory

Yacine Ait-Sahalia·Per A. Mykland
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Abstract

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are discretely sampled at a fixed nonrandom time interval. We include as specific examples estimators based on maximum-likelihood and discrete approximations such as the Euler scheme.

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Yacine Ait-Sahalia, Per A. Mykland. 2005-03-29. Estimators of diffusions with randomly spaced discrete observations: A general theory. https://doi.org/10.1214/009053604000000427

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