## Bernoulli

• Bernoulli
• Volume 15, Number 4 (2009), 1222-1242.

### On the approximation of mean densities of random closed sets

#### Abstract

Many real phenomena may be modelled as random closed sets in $ℝ^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n≤d$ in spaces of dimension $d≥1$, several problems are related to the estimation of such mean densities. In order to confront such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze an approximation of mean densities for sufficiently regular random closed sets. We show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to illustrate various relevant situations.

#### Article information

Source
Bernoulli, Volume 15, Number 4 (2009), 1222-1242.

Dates
First available in Project Euclid: 8 January 2010

https://projecteuclid.org/euclid.bj/1262962233

Digital Object Identifier
doi:10.3150/09-BEJ186

Mathematical Reviews number (MathSciNet)
MR2597590

Zentralblatt MATH identifier
1253.60007

#### Citation

Ambrosio, Luigi; Capasso, Vincenzo; Villa, Elena. On the approximation of mean densities of random closed sets. Bernoulli 15 (2009), no. 4, 1222--1242. doi:10.3150/09-BEJ186. https://projecteuclid.org/euclid.bj/1262962233

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