A renewal theorem in the finite-mean case

Abstract

Let F(.) be a c.d.f. on (0, oo) such that F(.) 1F(.) is regularly varying with exponent -ce, 1 < co < 2. Then U(t) ff F(v)dvds = O(t4F(t)2F(t2F(t))) as t -+ oo, where U(t) = EN(t) is the renewal function associated with F(t). Moreover similar estimates are given for distributions in the domain of attraction of the normal distribution and for the variance of N(t). The estimates improve earlier results of Teugels and Mohan.