Open Access
February, 1983 Remainder Term Estimates of the Renewal Function
Hasse Carlsson
Ann. Probab. 11(1): 143-157 (February, 1983). DOI: 10.1214/aop/1176993664


Let $\mu$ be a probability measure and $H(x) = \sum^\infty_{n=0} \mu^{n_\ast}(-\infty, x\rbrack$ its renewal function. It is well-known that $H(x) - x/\mu_1 - \mu_2/2\mu^2_1 \rightarrow 0$ as $x \rightarrow +\infty$ if $\mu_1 > 0$ and $\mu$ is a nonlattice measure. ($\mu_k$ is the $k$th moment of $\mu$.) The rate of this convergence is studied under further conditions on $\mu$.


Download Citation

Hasse Carlsson. "Remainder Term Estimates of the Renewal Function." Ann. Probab. 11 (1) 143 - 157, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0507.60081
MathSciNet: MR682805
Digital Object Identifier: 10.1214/aop/1176993664

Primary: 60K05

Keywords: Renewal function , renewal theory

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
Back to Top