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

Yacine Ait-Sahalia, Per A. Mykland

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2186-2222
Number of pages37
JournalAnnals of Statistics
Issue number5
StatePublished - Oct 2004

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Diffusions
  • Discrete and random sampling
  • Likelihood


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