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Wiener-Hopf methods, decompositions, and factorisation identities for maxima and minima of homogeneous random processes

Published online by Cambridge University Press:  01 July 2016

Priscilla Greenwood
Priscilla Greenwood*
Affiliation:
University of British Columbia
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Abstract

Some Wiener-Hopf type results are collected, related and given more direct proofs. Spitzer's random-walk method for the Wiener-Hopf integral equation also produces his factorisation relating functionals of maxima and minima. Transform equations are interpreted as decompositions of time-changed processes. Discrete- and continuous-time versions are related. Prabhu's factorisation for generators is equivalent to Fristedt's Lévy measure factorisation and to process decomposition.

Keywords

RANDOM WALKHOMOGENEOUS PROCESSMAXIMA AND MINIMAWIENER-HOPFFACTORISATION IDENTITIESSTOPPING TIMES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 4 , December 1975 , pp. 767 - 785
Copyright
Copyright © Applied Probability Trust 1975 

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