## 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 language | American English |
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Pages (from-to) | 749-774 |

Number of pages | 26 |

Journal | Annals of Applied Probability |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1998 |

## Keywords

- Overshoot
- Sequential test
- Time series