Second-order renewal theorem in the finite-means case

Abstract:

Let F be a distribution function (d.f.) on (0, ∞) and let U be the renewal function associated with F. If F has a finite first moment μ, then it is well known that U(t) asymptotically equals t/μ. It is also well known that U(t) - t/μ asymptotically behaves as S(t)/μ, where S denotes the integral of the integrated tail distribution F1 of F. In this paper we discuss the rate of convergence of U(t) - t/μ -S(t)/μ, for a large class of distribution functions. The estimate improves earlier results of Geluk, Teugels, and Embrechts and Omey.

Año de publicación:

2003

Keywords:

• O-regular variation
• Subexponential distributions
• Regular variation
• Renewal function

Fuente:

scopus