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An alternative to Wiener-Hopf methods for the study of bounded processes

Published online by Cambridge University Press:  14 July 2016

J. Keilson
J. Keilson*
Affiliation:
Sylvania Electronic Systems, Waltham, Massachusetts
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Homogeneous additive processes on a finite or semi-infinite interval have been studied in many forms. Wald's identity for the first passage process on the finite interval (see for example Miller, 1961), the waiting time process of Lindley (1952), and a variety of problems in the theory of queues, dams, and inventories come to mind. These processes have been treated by and large by methods in the complex plane. Lindley's discrete parameter process on the continuum, for example, described by where the ξn are independent identically distributed random variables, has been discussed by Wiener-Hopf methods in recent years by Lindley (1952), Smith (1953), Kemperman (1961), Keilson (1961), and many others. A review of earlier studies is given by Kemperman.

Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 1 , June 1964 , pp. 85 - 120
Copyright
Copyright © Applied Probability Trust 1964 

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