On asymptotic solutions of the renewal equation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)243-250
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume53
Issue number2
Publication statusPublished - Feb 1976
Externally publishedYes

Abstract

Consider the renewal equation in the form (*) u(t) = g(t) + ∝o t u(t - τ) f{hook}(τ) dτ, where f{hook}(t) is a probability density on [0, ∞) and limt → ∞ g(t) = g0. Asymptotic solutions of (*) are given in the case when f(t) has no expectation, i.e., ∝0 tf{hook}(t)dt = ∞. These results complement the classical theorem of Feller under the assumption that f(t) possesses finite expectation. © 1976.