BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Laboratoire de Mathématiques de Versailles - ECPv6.3.5//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Laboratoire de Mathématiques de Versailles X-ORIGINAL-URL:https://lmv.math.cnrs.fr X-WR-CALDESC:évènements pour Laboratoire de Mathématiques de Versailles REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:Europe/Paris BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:20210328T010000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:20211031T010000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=Europe/Paris:20210316T113000 DTEND;TZID=Europe/Paris:20210316T123000 DTSTAMP:20240329T091128 CREATED:20210118T121214Z LAST-MODIFIED:20210318T102953Z UID:8913-1615894200-1615897800@lmv.math.cnrs.fr SUMMARY:PS : Ester Mariucci (LMV) Nonparametric estimation of the Lévy density from high frequency observations DESCRIPTION:Résumé : \nWe consider the problem of estimating the Lévy density $f$ of a pure jump Lévy process\, possibly of infinite variation\, from the high frequency observation of one trajectory. We discuss two different approaches. \nThe first one consists in reducing the problem of the nonparametric estimation of $f$ to an easier one\, namely the estimation of a drift of a Gaussian white noise model. \nMore precisely\, we establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time $T$\, with $T$ tending to $\infty$. These approximations are given in the sense of the Le Cam distance\, under some smoothness conditions on the unknown Lévy density. The asymptotic equivalences are established by constructing explicit equivalence mappings that can be used to reproduce one experiment from the other and to transfer estimators. \nThe second approach consists in directly constructing an estimator of the Lévy density. For that we use a compound Poisson approximation and we build a linear wavelet estimator. Its performance is studied in terms of $L_p$ loss functions\, $p\geq1$\, over Besov balls. The resulting rates are minimax-optimal for a large class of Lévy processes. \nTravail en collaboration avec Céline Duval (MAP5\, Paris). \nExposé en mode hybride  : oratrice et partie du public au LMV + retransmission en visio (lien Zoom sur demande) \n  \nPS : Ester Mariucci (LMV) Nonparametric estimation of the Lévy density from high frequency observations URL:https://lmv.math.cnrs.fr/evenenement/ps-ester-mariucci-lmv-nonparametric-estimation-of-the-levy-density-from-high-frequency-observations/ CATEGORIES:Séminaire PS END:VEVENT END:VCALENDAR