On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes
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LetX= {Xt:t≥ 0} be a stationary piecewise continuousRd-valued process that moves between jumps along the integral curves of a given continuous vector field, and letS⊂Rdbe a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings ofSbyXto the distribution ofX0. Our result is illustrated by examples relating to queueing networks and stress release network models.
2012 ◽
Vol 49
(2)
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pp. 351-363
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2009 ◽
Vol 14
(9)
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pp. 1044-1045
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1986 ◽
Vol 33
(3)
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pp. 407-418
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2008 ◽
Vol 13
(9)
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pp. 776-780
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2021 ◽
Vol 9
(2)
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pp. 731-762