Year: 2010
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Borovkov, K. A., Last, G.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4307448005