Open Access
August, 1992 On Moments of the First Ladder Height of Random Walks with Small Drift
Joseph T. Chang
Ann. Appl. Probab. 2(3): 714-738 (August, 1992). DOI: 10.1214/aoap/1177005656


This paper presents some results that are useful in the study of asymptotic approximations of boundary crossing probabilities for random walks. The main result is a refinement of an asymptotic expansion of Siegmund concerning moments of the first ladder height of random walks having small positive drift. An analysis of the covariance between the first passage time and the overshoot of a random walk over a horizontal boundary contributes to the development of the main result and is of independent interest as well. An application of these results to a "moderate deviations" approximation for the probability distribution of the time to false alarm in the cusum procedure is briefly described.


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Joseph T. Chang. "On Moments of the First Ladder Height of Random Walks with Small Drift." Ann. Appl. Probab. 2 (3) 714 - 738, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0760.60064
MathSciNet: MR1177906
Digital Object Identifier: 10.1214/aoap/1177005656

Primary: 60J15
Secondary: 60F99 , 62L10

Keywords: boundary crossing probability , corrected diffusion approximation , cusum procedure , exponential family , first ladder height , First passage time , Moderate deviations , overshoot , Random walk , uniform renewal theorem

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
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