The Annals of Mathematical Statistics

An Upper Bound for the Renewal Function

Charles J. Stone

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Abstract

In this note we show that the renewal function $H$ corresponding to a random walk with positive mean $\mu$ and finite variance $\sigma^2$ satisfies the inequality $H(x) < \mu^{-1} x + 3(1 + \mu^{-2}\sigma^2)$.

Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 2050-2052.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177690883

Digital Object Identifier
doi:10.1214/aoms/1177690883

Mathematical Reviews number (MathSciNet)
MR356270

Zentralblatt MATH identifier
0257.60030

JSTOR
links.jstor.org

Citation

Stone, Charles J. An Upper Bound for the Renewal Function. Ann. Math. Statist. 43 (1972), no. 6, 2050--2052. doi:10.1214/aoms/1177690883. https://projecteuclid.org/euclid.aoms/1177690883


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