A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations

Benjamin Yakir*, Moshe Pollak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The probability that a stochastic process with negative drift exceed a value a often has a renewal-theoretic approximation as a → ∞. 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 ∞ 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.

Original languageAmerican English
Pages (from-to)749-774
Number of pages26
JournalAnnals of Applied Probability
Volume8
Issue number3
DOIs
StatePublished - Aug 1998

Keywords

  • Overshoot
  • Sequential test
  • Time series

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