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Estimators of diffusions with randomly spaced discrete observations: a general theory. (English) Zbl 1062.62155

Summary: 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.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
60J60 Diffusion processes
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