Fluctuations of random walk in R d and storage systems
- 1 March 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (03) , 566-587
- https://doi.org/10.1017/s0001867800028986
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 R d . 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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