### Abstract

Original language | English |
---|---|

Article number | 1708.02408 |

Number of pages | 22 |

Journal | arXiv |

Issue number | 1708.02408 |

Publication status | Published - 9 Aug 2017 |

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### Cite this

*arXiv*, (1708.02408), [1708.02408].

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*arXiv*, no. 1708.02408, 1708.02408.

**First-passage time asymptotics over moving boundaries for random walk bridges.** / Sloothaak, F.; Zwart, B.; Wachtel, V.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - First-passage time asymptotics over moving boundaries for random walk bridges

AU - Sloothaak, F.

AU - Zwart, B.

AU - Wachtel, V.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge. In the latter case, a phase transition appears in the asymptotics, of which the precise nature depends on the order of distance between zero and the moving boundary.

AB - We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge. In the latter case, a phase transition appears in the asymptotics, of which the precise nature depends on the order of distance between zero and the moving boundary.

M3 - Article

JO - arXiv

JF - arXiv

IS - 1708.02408

M1 - 1708.02408

ER -