Integral representations and convergence of the renewal density

• Published in: Journal of mathematical analysis and applications Vol. 323; no. 2; pp. 974 - 984
• Main Author: Stadje, Wolfgang
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.11.2006; Elsevier
• Subjects: Asymptotic behavior; Distribution theory; Exact sciences and technology; Fourier analysis; Fourier transform; Global analysis, analysis on manifolds; Integral representation; Mathematical analysis; Mathematics; Probability and statistics; Probability theory and stochastic processes; Renewal density; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Fourier transform; Integral representation; Asymptotic behavior; Renewal density; Probability density; Fourier transformation; Mathematical analysis; Integrability; Half plane; Integral representatior; Probability distribution; Convergence

We derive integral representations for the renewal density u associated with a square integrable probability density p on [ 0 , ∞ ) having finite expected value μ. These representations express u in terms of the real and the imaginary part of the Fourier transform of p, considered as a function on t...