A strong renewal theorem for generalized renewal functions in the infinite mean case

Summary LetF(x) be a nonarithmetic c.d.f. on (0, ) such that 1 —F(x)=x^–L(x), whereL(x) is slowly varying and 01. Leta(x) be regularly varying with exponent 1. A strong renewal theorem (of Blackwell type) for generalized renewal functions of the form is proved here, thus extending the recent work of Embrechts, Maejima and Omey [1] and that of Erickson [4].Kevin K. Anderson is now at Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 914550 USA. His research was performed in part under the auspices of the U.S. Department of Energy at LLNL under Contract W-7405-Eng-48.The research of Krishna B. Athreya was supported in part by NSF Grants DMS-8502311 and DMS-8706319.