BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Estimation of the Lévy measure: statistical inverse problem and D
 onsker Theorem - Markus Reiß\, Humboldt-Universität zu Berlin
DTSTART:20140624T134500Z
DTEND:20140624T141500Z
UID:TALK53107@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:We consider estimation of the characteristics of a Lévy proce
 ss from discrete time\nobservations. When the distance in observation time
  does not tend to zero\, we face\na nonlinear statistical inverse problem 
 (that of decompounding in the compound\nPoisson case) with the Lévy measu
 re as a nonparametric quantity. We shall\nconcentrate on the generalized d
 istribution function of the Lévy measure and show\nthat a Donsker theorem
  or uniform CLT is feasible provided the characteristic\nfunctions does no
 t decay too fast. Interestingly\, for both\, the pointwise CLT and the\nti
 ghtness part\, we need advanced Fourier analysis (multiplier theorems\, Be
 sov\nspaces). Smoothed empirical processes\, as introduced by Giné and Ni
 ckl (2008)\, will\nprove to be an essential ingredient.\nJoint work with R
 ichard Nickl.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
END:VEVENT
END:VCALENDAR