Doney, R. A. and Maller, R. A.
(2006)
*Almost Sure Relative Stability of the
Overshoot of Power Law Boundaries.*
[MIMS Preprint]

PDF
psrr17-2005.pdf Download (190kB) |

## 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 |
---|---|

Uncontrolled Keywords: | Random walk, curved boundaries, overshoot of power law boundaries |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes |

Depositing User: | Dr Peter Neal |

Date Deposited: | 12 Apr 2006 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/214 |

### Actions (login required)

View Item |