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DTSTART;TZID=Europe/Paris:20250404T100000
DTEND;TZID=Europe/Paris:20250404T110000
DTSTAMP:20260422T175244
CREATED:20240912T211517Z
LAST-MODIFIED:20250404T100657Z
UID:13137-1743760800-1743764400@lmv.math.cnrs.fr
SUMMARY:PS : Taher Jalal (LMV) : Non-parametric inference for Lévy processes with infinite jump activity
DESCRIPTION:Lévy processes with infinite jump activity present intricate stochastic dynamics. In this work\, we focus on the non-parametric estimation of the increment density for both the entire process and the small-jump component. We develop spectral estimators\, establish their convergence rates\, and achieve minimax optimality.  This study is conducted under various observation regimes\, including low- and high-frequency observations and with or without a Brownian component. Additionally\, we construct adaptive estimators and assess their performance through numerical studies on α-stable and tempered stable Lévy processes. Our results enhance statistical inference techniques for stochastic models driven by jump processes.
URL:https://lmv.math.cnrs.fr/evenenement/ps-taher-jalal-lmv/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire PS
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DTSTART;TZID=Europe/Paris:20250404T113000
DTEND;TZID=Europe/Paris:20250404T123000
DTSTAMP:20260422T175244
CREATED:20240912T211718Z
LAST-MODIFIED:20250404T100702Z
UID:13139-1743766200-1743769800@lmv.math.cnrs.fr
SUMMARY:PS : Jakob Söhl (TU Delft) : Spectral calibration of time-inhomogeneous exponential Lévy models
DESCRIPTION:Empirical evidence shows that calibrating exponential Lévy models by options with different maturities leads to conflicting information. In other words\, the stationarity implicitly assumed in the exponential Lévy model is not satisfied. An identifiable time-inhomogeneous Lévy model is proposed that does not assume stationarity and that can integrate option prices from different maturities and different strike prices without leading to conflicting information. In the time-inhomogeneous Lévy model\, the convergence rates are derived\, and confidence intervals are shown for the estimators of the volatility\, the drift\, the intensity and the Lévy density. Previously\, confidence intervals have been constructed for time-homogeneous Lévy models in an idealized Gaussian white noise model. In the idealized Gaussian white noise model\, it is assumed that the observations are Gaussian and given continuously across the strike prices. This simplifies the analysis significantly. The confidence intervals are constructed in a discrete observation setting for time-inhomogeneous Lévy models\, and the only assumption on the errors is that they are sub-Gaussian. In particular\, all bounded errors with arbitrary distributions are covered. Additional results on the convergence rates extend existing results from time-homogeneous to time-inhomogeneous Lévy models.
URL:https://lmv.math.cnrs.fr/evenenement/ps-jakob-sohl-tu-delft/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire PS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20250411T100000
DTEND;TZID=Europe/Paris:20250411T110000
DTSTAMP:20260422T175244
CREATED:20240912T112700Z
LAST-MODIFIED:20250411T134501Z
UID:13130-1744365600-1744369200@lmv.math.cnrs.fr
SUMMARY:PS : Jérôme Dedecker (Université Paris Cité\, MAP5) : Coefficients de couplage pour la marche aléatoire sur GL_d(R)
DESCRIPTION:Nous donnons des estimées pour des coefficients de couplage d’une suite stationnaire associée à la marche aléatoire sur GL_d(R). Nous montrons ensuite comment ces coefficients peuvent être utilisés pour obtenir des résultats limite pour cette marche\, sous des conditions de moments “naturelles”. Travaux en collaboration avec C. Cuny\, C. Jan et F. Merlevède.
URL:https://lmv.math.cnrs.fr/evenenement/ps-jerome-dedecker-universite-paris-cite-map5/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire PS
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DTSTART;TZID=Europe/Paris:20250411T113000
DTEND;TZID=Europe/Paris:20250411T123000
DTSTAMP:20260422T175244
CREATED:20240904T165405Z
LAST-MODIFIED:20250411T134508Z
UID:13104-1744371000-1744374600@lmv.math.cnrs.fr
SUMMARY:PS : Ronan Le Guevel (Université Rennes 2) : Estimation non-paramétrique de l'intensité de sauts d'un processus Birth-Death-Move
DESCRIPTION:Nous présentons un processus spatial de naissances et morts avec mouvement\, où la dynamique des naissances et des morts dépend de la configuration spatiale actuelle de la population et des déplacements possibles des individus au cours de leur vie. Nous abordons ensuite quelques propriétés probabilistes de ce processus (en particulier la propriété de Feller et l’ergodicité du processus). Nous donnons enfin une méthode non paramétrique à noyau pour l’estimation de la fonction d’intensité de saut du processus. Travail en collaboration avec E. Manent et F. Lavancier (ENSAI).
URL:https://lmv.math.cnrs.fr/evenenement/ps-ronan-le-guevel-universite-rennes-2/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire PS
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