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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/

[1] B.M. Bibby and M. Sørensen, Martingale estimation functions for discretely observed diffusion processes, Bernoulli 1 (1995), 17-39.

[2] U. Küchler and M. Sørensen, Exponential Families of Stochastic Processes, Springer-Verlag 1997.

[3] S. Iacus, Simulation and Inference for Stochastic Differential, Equations with R Examples, Springer 2008.

[4] J.T. Mexia and G.C. Dias, Statistical Inference for Discretely Observed Diffusions of Diffusions, VII-Congresso da SPE, 14-16 Outubro, Osir 1999.

[5] B. Øksendal, Stochastic Differential Equations, An Introduction, Fifth Edition, Springer-Verlag 1998.

[6] M. Sørensen, Lecture Notes on 'Statistical Inference for Discretely Observed Diffusions', Berlin Graduiertenkolleg 1998.