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

Per A. Mykland, Yacine A�t-Sahalia
2004 Annals of Statistics  
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
more » ... ely 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.
doi:10.1214/009053604000000427 fatcat:wtxuljptlzgvdgbjpkp4lg4d4q