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February, 1979 Envelopes of Vector Random Processes and Their Crossing Rates
Daniele Veneziano
Ann. Probab. 7(1): 62-74 (February, 1979). DOI: 10.1214/aop/1176995148


Vector-valued random processes, $\mathbf{X}(t)$, can be "enveloped" by set-valued random processes, $\mathscr{S}(t)$, to which they belong with probability 1 during any finite length of time. When applied to scalar processes, the set-definition of envelope includes and is richer than the familiar point-definitions. Several random set-envelope processes in $n$-dimensional space, $R_n$, are defined and the mean rates at which they "cross" given regions of $R_n$ are calculated. Comparison is made with the mean crossing rates of associated enveloped Gaussian processes, $\mathbf{X}(t)$.


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Daniele Veneziano. "Envelopes of Vector Random Processes and Their Crossing Rates." Ann. Probab. 7 (1) 62 - 74, February, 1979.


Published: February, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0403.60036
MathSciNet: MR515813
Digital Object Identifier: 10.1214/aop/1176995148

Primary: 60G10

Keywords: envelopes , first crossing , reliability , Stochastic vector processes

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 1 • February, 1979
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