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August 1998 A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations
Moshe Pollak, Benjamin Yakir
Ann. Appl. Probab. 8(3): 749-774 (August 1998). DOI: 10.1214/aoap/1028903449

Abstract

The probability that a stochastic process with negative drift exceed a value a often has a renewal-theoretic approximation as $a \to \infty$. Except for a process of iid random variables, this approximation involves a constant which is not amenable to analytic calculation. Naive simulation of this constant has the drawback of necessitating a choice of finite a, thereby hurting assessment of the precision of a Monte Carlo simulation estimate, as the effect of the discrepancy between a and $\infty$ is usually difficult to evaluate.

Here we suggest a new way of representing the constant. Our approach enables simulation of the constant with prescribed accuracy. We exemplify our approach by working out the details of a sequential power one hypothesis testing problem of whether a sequence of observations is iid standard normal against the alternative that the sequence is AR(1). Monte Carlo results are reported.

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Moshe Pollak. Benjamin Yakir. "A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations." Ann. Appl. Probab. 8 (3) 749 - 774, August 1998. https://doi.org/10.1214/aoap/1028903449

Information

Published: August 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0937.60082
MathSciNet: MR1627779
Digital Object Identifier: 10.1214/aoap/1028903449

Subjects:
Primary: 60K05
Secondary: 62L10

Keywords: overshoot , sequential test , time series

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 3 • August 1998
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