Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/56623 
Year of Publication: 
2012
Series/Report no.: 
SFB 649 Discussion Paper No. 2012-003
Publisher: 
Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, Berlin
Abstract: 
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.
Subjects: 
uniform central limit theorem
nonlinear inverse problem
smoothed empirical processes
pseudo-differential operators
jump measure
JEL: 
C14
C22
Document Type: 
Working Paper

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