Stochastic models as functionals: Some remarks on the renewal case

The standard stochastic model of renewal theory is regarded as a functional which associates with a lifetime distribution μ the corresponding renewal measure ν=Σ−r•â0âμ*ⁿ. The behaviour of this functional near exponential distributions is investigated. The literature mainly deals with the asymptotic behaviour of ν([0,t]) and ν([t,t+1]) as t⇒•-this new approach leads to expansions which are valid uniformly in t∈ℝ.