# Nonparametric estimation for stochastic differential equations with random effects

Abstract : We consider $N$ independent stochastic processes $(X_j(t), t\in [0,T])$, $j=1, \ldots,N$, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable $\phi_j$ and study the nonparametric estimation of the density of the random effect $\phi_j$ in two kinds of mixed models. A multiplicative random effect and an additive random effect are successively considered. In each case, we build kernel and deconvolution estimators and study their $L^2$-risk. Asymptotic properties are evaluated as $N$ tends to infinity for fixed $T$ or for $T=T(N)$ tending to infinity with $N$. For $T(N)=N^2$, adaptive estimators are built. Estimators are implemented on simulated data for several examples.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2013, 123 (7), pp.2522-2551. <10.1016/j.spa.2013.04.009>
Domaine :

https://hal.archives-ouvertes.fr/hal-00761394
Contributeur : Fabienne Comte <>
Soumis le : mercredi 5 décembre 2012 - 14:16:59
Dernière modification le : mardi 11 octobre 2016 - 12:01:38
Document(s) archivé(s) le : mercredi 6 mars 2013 - 17:05:09

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MixedEDS_3_.pdf
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### Citation

Fabienne Comte, Valentine Genon-Catalot, Adeline Samson. Nonparametric estimation for stochastic differential equations with random effects. Stochastic Processes and their Applications, Elsevier, 2013, 123 (7), pp.2522-2551. <10.1016/j.spa.2013.04.009>. <hal-00761394>

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