## 2006.59: Almost Sure Relative Stability of the Overshoot of Power Law Boundaries

2006.59:
R. A. Doney and R. A. Maller
(2006)
*Almost Sure Relative Stability of the
Overshoot of Power Law Boundaries.*

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## Abstract

We give necessary and sufficient conditions for the almost sure (a.s.) relative stability of the overshoot of a random walk when it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, ±rn^b, r > 0, n = 1, 2, · · · , where 0 ≤ b < 1, b 6= 1/2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and nonzero, or the step length has a finite variance and mean zero.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | Random walk, curved boundaries, overshoot of power law boundaries |

Subjects: | MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2006.59 |

Deposited By: | Dr Peter Neal |

Deposited On: | 12 April 2006 |

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