### Abstract

We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. © Institute of Mathematical Statistics, 2005.

Original language | English |
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Pages (from-to) | 1936-1957 |

Number of pages | 22 |

Journal | Annals of Applied Probability |

Volume | 15 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 2005 |

### Keywords

- Boundary
- Random walk
- Ruin probability
- Subexponential distributions

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## Cite this

Fos, S., Palmowski, Z., & Zachary, S. (2005). The probability of exceeding a High boundary on a random time interval for a heavy-tailed random walk.

*Annals of Applied Probability*,*15*(3), 1936-1957. https://doi.org/10.1214/105051605000000269