Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T03:19:09.444Z Has data issue: false hasContentIssue false

Tail behaviour of ladder-height distributions in random walks

Published online by Cambridge University Press:  14 July 2016

Rudolf Grübel*
Affiliation:
University of Essen
*
Postal address: Universität Essen-GHS, Fachbereich 6 (Mathematik), Universitätsstr. 3, D-4300 Essen, West Germany.

Abstract

We give necessary and sufficient conditions for various results connecting the tail behaviour of a distribution with that of its right Wiener–Hopf factor.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Doney, R. A. (1980) Moments of ladder heights in random walks. J. Appl. Prob. 17, 248252.CrossRefGoogle Scholar
[2] Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979) Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335347.Google Scholar
[3] Feller, W. (1971) An Introduction to Probability Theory and Its Applications, II. Wiley, New York.Google Scholar
[4] De Haan, L. (1970) On Regular Variation and its Application to the Weak Convergence of Sample Extremes. Mathematical Centre Tract 32, Amsterdam.Google Scholar
[5] Rogozin, R. A. (1964) On the distribution of the first jump. Theory Prob. Appl. 9, 450465.CrossRefGoogle Scholar
[6] Veraverbeke, N. (1977) Asymptotic behaviour of Wiener–Hopf factors of a random walk. Stoch. Proc. Appl. 5, 2737.Google Scholar