Renewal theory with infinite mean

Ron Doney (University of Manchester)

Franks Adams 2,

A long-standing problem, going back to work by Garsia and Lamperti, Erickson and Williamson in the 1960s, concerns the asymptotic behaviour of the renewal mass function in the case that the step distribution is in the domain of attraction of a stable law of index 0<α≤ 1/2. In this talk I will survey the existing literature and describe a new technique, based on an estimate of the error term in the classical local limit theorems.

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