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April, 1989 A Renewal Theory with Varying Drift
Cun-Hui Zhang
Ann. Probab. 17(2): 723-736 (April, 1989). DOI: 10.1214/aop/1176991423

Abstract

Let $R$ be the excess over the boundary in renewal theory. It is well known that $ER$ has a limit $r$ when the drift of the random walk $\mu \geq 0$. We study renewal theorems with varying $\mu$. Conditions are given under which the tail $ER - r$ is uniformly dominated by a decreasing integrable function for $\mu$ in a compact interval in $(0, \infty)$. Conditions are also given under which the derivative of the tail $(\partial/\partial\mu)(ER - r)$ is uniformly dominated by a directly Riemann integrable function.

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Cun-Hui Zhang. "A Renewal Theory with Varying Drift." Ann. Probab. 17 (2) 723 - 736, April, 1989. https://doi.org/10.1214/aop/1176991423

Information

Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0676.60080
MathSciNet: MR985386
Digital Object Identifier: 10.1214/aop/1176991423

Subjects:
Primary: 60K05
Secondary: 60G40

Keywords: excess over the boundary , Fourier transformation , renewal theory , Uniform convergence

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • April, 1989
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