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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1124,
author = {Lu\'\i s Ramos},
title = {Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {30},
year = {2010},
pages = {117-122},
zbl = {1208.62130},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1124}
}
Luís Ramos. Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion. Discussiones Mathematicae Probability and Statistics, Tome 30 (2010) pp. 117-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1124/
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