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October 1996 On some boundary crossing problems for Gaussian random walks
V. I. Lotov
Ann. Probab. 24(4): 2154-2171 (October 1996). DOI: 10.1214/aop/1041903223

Abstract

We consider random walks with Gaussian distribution of summands. New representations for Wiener-Hopf factorization components are obtained. The factorization method is used to study the distribution of the excess over one-sided and two-sided boundaries. Asymptotic expansions for these distributions and for the expectation of the first exit time are obtained under the assumption that the boundaries tend to infinity.

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V. I. Lotov. "On some boundary crossing problems for Gaussian random walks." Ann. Probab. 24 (4) 2154 - 2171, October 1996. https://doi.org/10.1214/aop/1041903223

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0876.60057
MathSciNet: MR1415246
Digital Object Identifier: 10.1214/aop/1041903223

Subjects:
Primary: 60J15
Secondary: 60G40 , 60G50

Keywords: first exit time , overshoot , Random walks , sequential probability ratio test , Wiener-Hopf factorization

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • October 1996
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