Geodesic
Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points
Serdica Mathematical Journal, Tome 31 (2005) no. 4, pp. 291-308

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In this paper, we study the quasi-likelihood estimator of the drift parameter θ 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 θ, 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.
Keywords: Diffusion Processes, Ornstein-Uhlenbeck, Quasi-Likelihood, Poisson Arrivals 
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     title = {Quasi-Likelihood {Estimation} for {Ornstein-Uhlenbeck} {Diffusion} {Observed} at {Random} {Time} {Points}},
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Adès, Michel; Dion, Jean-Pierre; MacGibbon, Brenda. Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points. Serdica Mathematical Journal, Tome 31 (2005) no. 4, pp. 291-308. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_4_a2/