Nonparametric trend coefficient estimation for multidimensional diffusions

Annamaria Bianchi

doi:10.1016/j.crma.2007.05.012

Statistics

Nonparametric trend coefficient estimation for multidimensional diffusions
[Estimation non-paramétrique du terme de dérive dans un processus de diffusion multidimensionnel]

Présenté par : Paul Deheuvels

Annamaria Bianchi ¹

¹ Department of Mathematics, University of Milan, via Saldini 50, 20133 Milano, Italy

Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 101-105.

Résumé
Abstract

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 $L^{2}$ et presque sûr. Finalement, on donne à titre d'exemple une classe de processus qui satisfont nos hypothèses.

We consider the problem of the density and drift estimation by the observation of a trajectory of an $R^{d}$ 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.

Reçu le : 2006-02-10
Accepté le : 2007-04-27
Publié le : 2007-07-05

DOI : 10.1016/j.crma.2007.05.012

Affiliations des auteurs :

Annamaria Bianchi ¹

¹ Department of Mathematics, University of Milan, via Saldini 50, 20133 Milano, Italy

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     title = {Nonparametric trend coefficient estimation for multidimensional diffusions},
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     doi = {10.1016/j.crma.2007.05.012},
     language = {en},
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Annamaria Bianchi. Nonparametric trend coefficient estimation for multidimensional diffusions. Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 101-105. doi : 10.1016/j.crma.2007.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.012/

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Cité par

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Julien Apala N’drin; Ouagnina Hili Minimum Hellinger Distance Estimation for Discretely Observed Stochastic Processes Using Recursive Kernel Density Estimator, Journal of Statistical Theory and Practice, Volume 16 (2022) no. 3 | DOI:10.1007/s42519-022-00269-5
Julien Apala N’drin; Ouagnina Hili From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes, Applied Mathematics, Volume 06 (2015) no. 09, p. 1592 | DOI:10.4236/am.2015.69142
Annamaria Bianchi The normal approximation rate for the drift estimator of multidimensional diffusions, Statistical Inference for Stochastic Processes, Volume 12 (2009) no. 3, p. 251 | DOI:10.1007/s11203-008-9032-5

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