On asymptotic solutions of the renewal equation

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 lim_{t → ∞} 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.