Groupe d’études et de recherche en analyse des décisions

G-2005-55

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

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In this paper, we study the quasi-likelihood estimator of the drift parameter in the Ornstein-Uhlenbeck diffusion process, when the process is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of , as well as those of its approximations are also elucidated. An extensive simulation study of these estimators is also performed. As a corollary to this work, we obtain the quasi-likelihood estimator iteratively in the deterministic framework with non-equidistant time points.

, 22 pages

Ce cahier a été révisé en décembre 2005