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.
Publié le : 1976-12-14
Classification:
Expected first passage times,
Wiener process,
range of partial sums,
maximum waiting time,
detecting a change in a parameter,
average run length,
60F99,
60G50,
60K25,
62N10
@article{1176995948,
author = {Robbins, Naomi B.},
title = {Convergence of Some Expected First Passage Times},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 1027-1029},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995948}
}
Robbins, Naomi B. Convergence of Some Expected First Passage Times. Ann. Probab., Tome 4 (1976) no. 6, pp. 1027-1029. http://gdmltest.u-ga.fr/item/1176995948/