Liggett, Thomas M. Total positivity and renewal theory. (English) Zbl 0682.60078 Probability, statistics, and mathematics, Pap. in Honor of Samuel Karlin, 141-162 (1989). [For the entire collection see Zbl 0679.00013.] The paper unifies and considerably extends several known results on the relations between a probability density f and the corresponding renewal density u by means of total positivity. Moreover for a density f with decreasing failure rate there is given a straight forward proof of the fact that (in the discrete time formulation) \(u(n)-u(n+1)\) is asymptotic to a constant multiple of the tail probabilities of f. Reviewer: M.Schäl Cited in 6 Documents MSC: 60K05 Renewal theory Keywords:renewal density; total positivity; tail probabilities Citations:Zbl 0679.00013 PDFBibTeX XML