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October 2004 Estimators of diffusions with randomly spaced discrete observations: A general theory
Yacine Aït-Sahalia, Per A. Mykland
Ann. Statist. 32(5): 2186-2222 (October 2004). DOI: 10.1214/009053604000000427


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 Aït-Sahalia. Per A. Mykland. "Estimators of diffusions with randomly spaced discrete observations: A general theory." Ann. Statist. 32 (5) 2186 - 2222, October 2004.


Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1062.62155
MathSciNet: MR2102508
Digital Object Identifier: 10.1214/009053604000000427

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: Diffusions , discrete and random sampling , likelihood

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 5 • October 2004
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