On asymptotic solutions of the renewal equation

AbstractConsider the renewal equation in the form (∗) u(t) = g(t) + ∝ot u(t − τ) ƒ(τ) dτ, where ƒ(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∞ tƒ(t)dt = ∞. These results complement the classical theorem of Feller under the assumption that f(t) possesses finite expectation