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We consider the problem of the density and drift estimation by the observation of a trajectory of an dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type and study the mean-square and almost sure uniform asymptotic behavior for these estimators. Finally, we give a class of processes satisfying our assumptions.
On considère le problème de l'estimation de la densité et du terme de dérive par l'observation d'une trajectoire d'un processus de diffusion homogène en dimension d ayant une densité invariante unique. On construit les estimateurs par la méthode des noyaux, puis on en étudie le comportement asymptotique en et presque sûr. Finalement, on donne à titre d'exemple une classe de processus qui satisfont nos hypothèses.
Bianchi, Annamaria 1
@article{CRMATH_2007__345_2_101_0,
author = {Bianchi, Annamaria},
title = {Nonparametric trend coefficient estimation for multidimensional diffusions},
journal = {Comptes Rendus. Math\'ematique},
pages = {101--105},
publisher = {Elsevier},
volume = {345},
number = {2},
year = {2007},
doi = {10.1016/j.crma.2007.05.012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.05.012/}
}
TY - JOUR AU - Bianchi, Annamaria TI - Nonparametric trend coefficient estimation for multidimensional diffusions JO - Comptes Rendus. Mathématique PY - 2007 SP - 101 EP - 105 VL - 345 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.05.012/ DO - 10.1016/j.crma.2007.05.012 LA - en ID - CRMATH_2007__345_2_101_0 ER -
%0 Journal Article %A Bianchi, Annamaria %T Nonparametric trend coefficient estimation for multidimensional diffusions %J Comptes Rendus. Mathématique %D 2007 %P 101-105 %V 345 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.05.012/ %R 10.1016/j.crma.2007.05.012 %G en %F CRMATH_2007__345_2_101_0
Bianchi, Annamaria. Nonparametric trend coefficient estimation for multidimensional diffusions. Comptes Rendus. Mathématique, Tome 345 (2007) no. 2, pp. 101-105. doi : 10.1016/j.crma.2007.05.012. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.05.012/
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