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April, 1989 Sharp Rates for Increments of Renewal Processes
Paul Deheuvels, Josef Steinebach
Ann. Probab. 17(2): 700-722 (April, 1989). DOI: 10.1214/aop/1176991422

Abstract

Let $\{N(t), t \geq 0\}$ be the renewal process associated to an i.i.d. sequence $X_1, X_2, \ldots$ of nonnegative interarrival times having finite moment generating function near the origin. In this article we give strong and weak limiting laws for the maximal and minimal increments $\sup_{0 \leq t \leq T - K}(N(t + K) - N(t))$ and $\inf_{0 \leq t \leq T - k}(N(t + K) - N(t))$, where $K = K_T$ is a function of $T$ such that $0 \leq K_T \leq T$.

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Paul Deheuvels. Josef Steinebach. "Sharp Rates for Increments of Renewal Processes." Ann. Probab. 17 (2) 700 - 722, April, 1989. https://doi.org/10.1214/aop/1176991422

Information

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

zbMATH: 0679.60043
MathSciNet: MR985385
Digital Object Identifier: 10.1214/aop/1176991422

Subjects:
Primary: 60F15
Secondary: 60F05 , 60F17 , 60G55

Keywords: Invariance principles , Law of the iterated logarithm , laws of large numbers , renewal processes , weak laws

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • April, 1989
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