Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 8, Number 3 (1998), 749-774.
A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations
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.
Ann. Appl. Probab., Volume 8, Number 3 (1998), 749-774.
First available in Project Euclid: 9 August 2002
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Yakir, Benjamin; Pollak, Moshe. A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations. Ann. Appl. Probab. 8 (1998), no. 3, 749--774. doi:10.1214/aoap/1028903449. https://projecteuclid.org/euclid.aoap/1028903449