Integral representations and convergence of the renewal density

Autor(en): Stadje, Wolfgang 
Stichwörter: asymptotic behavior; Fourier transforrn; integral representation; Mathematics; Mathematics, Applied; renewal density
Erscheinungsdatum: 2006
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volumen: 323
Ausgabe: 2
Startseite: 974
Seitenende: 984
Zusammenfassung: 
We derive integral representations for the renewal density u associated with a square integrable probability density p on [0, infinity) having finite expected value mu. These representations express u in terms of the real and the imaginary part of the Fourier transform of p, considered as a function on the lower complex half plane. We use them to give simple global integrability conditions on p under which lim(t ->infinity) (u(t) - p(t)) = 1/mu. (c) 2005 Elsevier Inc. All rights reserved.
ISSN: 0022247X
DOI: 10.1016/j.jmaa.2005.11.003

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