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Moments of ladder heights in random walks

Published online by Cambridge University Press:  14 July 2016

R. A. Doney
R. A. Doney*
Affiliation:
University of Manchester
*
∗Postal address: Statistical Laboratory, Department of Mathematics, The University, Manchester M13 9PL, U.K.
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Abstract

A well-known result in the theory of random walks states that E{X2} is finite if and only if E{Z+} and E{Z_} are both finite (Z+ and Z_ being the ladder heights and X a typical step-length) in which case E{X2} = 2E{Z+}E{Z_}. This paper contains results relating the existence of moments of X of order ß to the existence of the moments of Z+ and Z_ of order ß – 1. The main result is that if β > 2 E{|X|β} < ∞ if and only if and are both finite.

Keywords

LADDER HEIGHTLADDER VARIABLELADDER EPOCHMOMENTSINEQUALITIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 248 - 252
Copyright
Copyright © Applied Probability Trust 1980 

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References

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