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Densities for stationary random sets and point processes

Published online by Cambridge University Press:  01 July 2016

Wolfgang Weil  and
John A. Wieacker
Wolfgang Weil*
Affiliation:
Universität Karlsruhe
John A. Wieacker*
Affiliation:
Universität Freiburg
*
∗ Postal address: Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe 1, West Germany.
∗∗ Postal address: Mathematisches Institut, Universität Freiburg, Hebelstrasse 29, 7800 Freiburg, West Germany.
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Abstract

For certain stationary random sets X, densities D φ (X) of additive functionals φ are defined and formulas for are derived when K is a compact convex set in . In particular, for the quermassintegrals and motioninvariant X, these formulas are in analogy with classical integral geometric formulas. The case where X is the union set of a Poisson process Y of convex particles is considered separately. Here, formulas involving the intensity measure of Y are obtained.

Keywords

QUERMASSINTEGRALSINTEGRAL GEOMETRIC FORMULAPOISSON PROCESS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 324 - 346
Copyright
Copyright © Applied Probability Trust 1984 

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