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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


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
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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