@techreport{Nickl2012Donsker,
abstract = {Given n equidistant realisations of a L\'{e}vy process (Lt; t >= 0), a natural estimator for the distribution function N of the L\'{e}vy 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 L\'{e}vy 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.},
address = {Berlin},
author = {Richard Nickl and Markus Rei\ss{}},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C14; C22; 330; uniform central limit theorem; nonlinear inverse problem; smoothed empirical processes; pseudo-differential operators; jump measure; Stochastischer Prozess; Sch\"{a}tztheorie; Theorie},
language = {eng},
number = {2012-003},
publisher = {SFB 649, Economic Risk},
title = {A Donsker theorem for L\'{e}vy measures},
type = {SFB 649 discussion paper},
url = {http://hdl.handle.net/10419/56623},
year = {2012}
}