Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions

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dc.creatorLoukianova, D.
dc.creatorLoukianov, O.
dc.date2008-08-22
dc.date.accessioned2026-07-07T09:57:57Z
dc.date.available2026-07-07T09:57:57Z
dc.descriptionUsually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach to the problem of non-parametric kernel drift estimation in the one-dimensional recurrent case. As a particular example we obtain the rate of convergence of the Nadaraya--Watson estimator in the case of a locally Hölder-continuous drift.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AIHP141 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0808.3069
dc.identifierhttp://arxiv.org/abs/0808.3069
dc.identifierAnnales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 4, 771-786
dc.identifierdoi:10.1214/07-AIHP141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167535
dc.subjectProbability
dc.titleUniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions
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