A note on mean volume and surface densities for a class of birth-and-growth stochastic processes

Details A note on mean volume and surface densities for a class of birth-and-growth stochastic processes A note on mean volume and surface densities for a class of birth-and-growth stochastic processes

2007-10-15

arxiv.org/abs/0710.2751v2

Mathematics

Probability

11 pages; revised version for publication: proof simplified, added new result

Scientific paper

Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as well as the so called mean \emph{extended} volume and surface densities, may be studied in terms of relevant quantities characterizing the process. We extend here known results in the Poissonian case to a wider class of birth-and-growth stochastic processes, proving in particular the absolute continuity of the random time of capture of a point $x\in\R^d$ by processes of this class.

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