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dc.contributor.authorRéveillac, Anthony
dc.contributor.authorPrivault, Nicolas
dc.subjectharmonic analysisen
dc.subjectMalliavin calculusen
dc.subjectGaussian spaceen
dc.subjectStein estimationen
dc.subjectNonparametric drift estimationen
dc.titleStochastic analysis on Gaussian space applied to drift estimationen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Loève expansions. We construct efficient estimators for the drift of such processes, and prove their minimaxity using Bayes estimators. We also construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and stochastic analysis on Gaussian space, in which superharmonic functionals of the process paths play a particular role. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolper.en
dc.publisher.nameUniversité de La Rochelleen
dc.publisher.cityLa Rochelleen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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