On Rice's formula for stationary multivariate piecewise smooth processes

Details On Rice's formula for stationary multivariate piecewise smooth processes On Rice's formula for stationary multivariate piecewise smooth processes

2010-09-20

arxiv.org/abs/1009.3885v1

Mathematics

Probability

Scientific paper

Let $X=\{X_t: t\ge 0\}$ be a stationary piecewise continuous $\R^d$-valued process that moves between jumps along the integral curves of a given continuous vector field, and let $S\subset\R^d$ be 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 of $S$ by $X$ to the distribution of $X_0$. Our result is illustrated by examples relating to queueing networks and stress release network models.

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