UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 37, Fasc. 2,
pages 291 - 298
 

RENEWAL FUNCTION ASYMPTOTICS REFINED Ŕ LA FELLER

Daryl Daley

Abstract: Feller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x → ∞ , the renewal function U (x ) of a renewal process with nonarithmetic generic lifetime X with finite mean E(X ) = 1∕λ and second moment differs from its linear asymptote λx by the quantity 1λ2E (X2 ) 2 . 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.

2010 AMS Mathematics Subject Classification: Primary: 60K05.

Keywords and phrases: Renewal function, asymptotics of refined iterates, moment condition.

Download:    Abstract    Full text   Abstract + References