## 2007.160: Passage times of random walks and Lévy processes across power law boundaries

2007.160:
R. A. Doney and R.A. Maller
(2005)
*Passage times of random walks and Lévy processes across power law boundaries.*
Probability Theory and Related Fields, 133 (1).
pp. 57-70.
ISSN 1432-2064

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DOI: 10.1007/s00440-004-0414-3

## Abstract

We establish an integral test involving only the distribution of the increments of a random walk S which determines whether limsup n→∞(S_n/n^κ) is almost surely zero, finite or infinite when 1/2 < κ < 1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now have quite explicit criteria for all values of κ≥0. The results, and those of [9], are also extended to Lévy processes.

Item Type: | Article |
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Uncontrolled Keywords: | Random walks - Lévy processes - Passage times - Exit times - Ladder processes - Power law boundaries - Limsup behaviour |

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

MIMS number: | 2007.160 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 19 November 2007 |

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