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Fluctuations of random walk in Rd and storage systems

Published online by Cambridge University Press:  01 July 2016

Priscilla Greenwood  and
Moshe Shaked
Priscilla Greenwood
Affiliation:
University of British Columbia
Moshe Shaked
Affiliation:
University of New Mexico
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Abstract

Two Wiener-Hopf type factorization identities for multivariate distributions are introduced. Properties of associated stopping times are derived. The structure that produces one factorization also provides the unique solution of the Wiener-Hopf convolution equation on a convex cone in Rd. Some applications for multivariate storage and queueing systems are indicated. For a few cases explicit formulas are obtained for the transforms of the associated stopping times. A result of Kemperman is extended.

Keywords

RANDOM WALKSTOPPING TIMESWIENER-HOPF FACTORIZATION
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 3 , September 1977 , pp. 566 - 587
Copyright
Copyright © Applied Probability Trust 1977 

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