On Rice's formula for stationary multivariate piecewise smooth processes (Q2897147)
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scientific article; zbMATH DE number 6053716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Rice's formula for stationary multivariate piecewise smooth processes |
scientific article; zbMATH DE number 6053716 |
Statements
8 July 2012
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level crossing
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Rice's formula
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stationarity
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Palm probability
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piecewise-deterministic process
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stochastic network
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On Rice's formula for stationary multivariate piecewise smooth processes (English)
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The authors extend Rice's formula (piecewise-smooth case) to a multivariate and non-Markovian cases. The result is different from the one obtained by \textit{K. Borovkov} and \textit{G. Last} [Adv. Appl. Probab. 40, No. 3, 815--834 (2008; Zbl 1177.60067)], where the proof relied on the Markov structure of the process and did not assume the existence of the density \(p\). Some examples related to queueing networks and stress release network models are presented.
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