The Annals of Statistics

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

Yacine Aït-Sahalia and Per A. Mykland

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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.

Article information

Ann. Statist., Volume 32, Number 5 (2004), 2186-2222.

First available in Project Euclid: 27 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators 62M05
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60

Diffusions likelihood discrete and random sampling


Aït-Sahalia, Yacine; Mykland, Per A. Estimators of diffusions with randomly spaced discrete observations: A general theory. Ann. Statist. 32 (2004), no. 5, 2186--2222. doi:10.1214/009053604000000427.

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