Please use this identifier to cite or link to this item:
Nickl, Richard
Reiß, Markus
Year of Publication: 
Series/Report no.: 
SFB 649 discussion paper 2012-003
Given n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.
uniform central limit theorem
nonlinear inverse problem
smoothed empirical processes
pseudo-differential operators
jump measure
Document Type: 
Working Paper

Files in This Item:
669.51 kB

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.