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

Doney, R. A. and Maller, R.A. (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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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
Uncontrolled Keywords:	Random walks - Lévy processes - Passage times - Exit times - Ladder processes - Power law boundaries - Limsup behaviour
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Ms Lucy van Russelt
Date Deposited:	19 Nov 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/901

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