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

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

2005-03-29

arxiv.org/abs/math/0503679v1

Annals of Statistics 2004, Vol. 32, No. 5, 2186-2222

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000427 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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