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December, 1976 Convergence of Some Expected First Passage Times
Naomi B. Robbins
Ann. Probab. 4(6): 1027-1029 (December, 1976). DOI: 10.1214/aop/1176995948


We discuss the convergence of the expected times until the partial sums of a sequence of independent, identically distributed random variables with zero means and unit variances first rise a height $h$ above their previous minimum as $h \rightarrow \infty$. We also consider the convergence as $r \rightarrow \infty$ of the expected times until the range of these partial sums exceeds a value $r$. Applications of these results to a quality control procedure and to queueing theory are mentioned.


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Naomi B. Robbins. "Convergence of Some Expected First Passage Times." Ann. Probab. 4 (6) 1027 - 1029, December, 1976.


Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0359.60055
MathSciNet: MR418248
Digital Object Identifier: 10.1214/aop/1176995948

Primary: 60F99
Secondary: 60G50 , 60K25 , 62N10

Keywords: average run length , detecting a change in a parameter , Expected first passage times , maximum waiting time , range of partial sums , Wiener process

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 6 • December, 1976
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