Renewal function asymptotics refined à la Feller

  1. Daryl Dalay

Abstract

 

RENEWAL FUNCTION ASYMPTOTICS REFINED À LA FELLER

Feller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x!1, the renewal function U(x) of a renewal process with nonarithmetic generic lifetime X with finite mean E(X)=1=and second moment differs from its linear asymptote x by the quantity 122E(X2). His first edition (1966) (but not the second in 1971) asserted that a similar approach would refine this asymptotic result when X has finite higher order moments. The paper shows how higher order moments may justify drawing conclusions from a recurrence relation that exploits a general renewal equation and further appeal to the Key Renewal Theorem.

 

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Probability and Mathematical Statistics

37, z. 2, 2017

Pages from 291 to 298

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