Fluctuations of random walk in Rd and storage systems
- 1 September 1977
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (3) , 566-587
- https://doi.org/10.2307/1426115
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
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