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UID:8710@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251007T143000
DTEND;TZID=Europe/Paris:20251007T153000
DTSTAMP:20250721T144046Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-220/
SUMMARY:Thị Bảo Trâm NGÔ  (Université d'Évry): Efficient estimation
  for stochastic differential equations driven by a stable Lévy process
DESCRIPTION:Thị Bảo Trâm NGÔ : The joint parametric estimation of the
  drift coefficient\,\nthe scale coefficient\, and the jump activity index\
 nin stochastic differential equations\ndriven by a symmetric stable Lévy 
 process\nis considered based on high-frequency observations.\nFirstly\, th
 e LAMN property for the corresponding Euler-type scheme is proven\,\nand l
 ower bounds for the estimation risk in this setting are deduced.\nTherefor
 e\, when the approximation scheme experiment is asymptotically equivalent\
 nto the high-frequency observation of the solution\nof the considered stoc
 hastic differential equation\,\nthese bounds can be transferred.\nSecondly
 \, since the maximum likelihood estimator can be time-consuming\nfor large
  samples\, an alternative Le Cam's one-step procedure is proposed\nin the 
 general setting.\nIt is based on an initial guess estimator\,\nwhich is a 
 combination of generalized variations\nof the trajectory for the scale and
  the jump activity index parameters\,\nand a maximum likelihood-type estim
 ator\nfor the drift parameter.\nThis proposed one-step procedure is shown 
 to be fast\,\nasymptotically normal\, and even asymptotically efficient\nw
 hen the scale coefficient is constant.\nIn addition\, the performances\nin
  terms of asymptotic variance and computation time\non samples of finite-s
 ize are illustrated with simulations.\nThis talk is based on joint work\nw
 ith Alexandre Brouste and Laurent Denis.
CATEGORIES:Séminaire,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
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  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20250330T030000
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