Geodesic
Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 117-122

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When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out.
Keywords: ergodic diffusions, martingale estimating functions, transition and invariant densities, maximum likelihood estimators 
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Ramos, Luís. Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 117-122. http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a6/