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On the local behaviour of ladder height distributions

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

J. Bertoin  and
R. A. Doney
J. Bertoin*
Affiliation:
Université Paris VI
R. A. Doney*
Affiliation:
University of Manchester
*
∗ Postal address: Laboratoire de Probabilités, Université Paris VI, t56, 4 Place Jussieu, 75252 Paris, France.
∗∗ Postal address: Statistical Laboratory, Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
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Abstract

There is a well-known connection between the asymptotic behaviour of the tail of the distribution of the increasing ladder height and the integrated tail of the step distribution of a random walk which either drifts to –∞, or oscillates and whose decreasing ladder height has finite mean. We establish a similar connection in a local sense; this means that in the lattice case we link the asymptotic behaviours of the mass function of the ladder height distribution and of the tail of the step distribution. We deduce the asymptotic behaviour of the mass function of the maximum of the walk, when this is finite, and also treat the non-lattice case.

Keywords

RANDOM WALKLADDER PHENOMENAMAXIMUMSUB-EXPONENTIALITY

MSC classification

Primary: 60E05: Distributions
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 816 - 821
Copyright
Copyright © Applied Probability Trust 1994 

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References

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