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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2006-02-10
Accepted: 2007-04-27
Published online: 2007-07-05

DOI: 10.1016/j.crma.2007.05.012

Author's affiliations:

Annamaria Bianchi ¹

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

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     author = {Annamaria Bianchi},
     title = {Nonparametric trend coefficient estimation for multidimensional diffusions},
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     pages = {101--105},
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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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