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A flow conservation law for surface processes

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

G. Last  and
R. Schassberger
G. Last*
Affiliation:
Technical University of Braunschweig
R. Schassberger*
Affiliation:
Technical University of Braunschweig
*
* Postal address for both authors: Institut für Mathematische Stochastik, Technische Universität Braunschweig, Pockelsstrasse 14, Postfach 3329, D-38106 Braunschweig, Germany.
* Postal address for both authors: Institut für Mathematische Stochastik, Technische Universität Braunschweig, Pockelsstrasse 14, Postfach 3329, D-38106 Braunschweig, Germany.
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Abstract

The object studied in this paper is a pair (Φ, Y), where Φ is a random surface in and Y a random vector field on . The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector field Y is smooth outside Φ but may have discontinuities on Φ. Gauss' divergence theorem is applied to derive a flow conservation law for Y. For this specializes to a well-known rate conservation law for point processes. As an application, relationships for the linear contact distribution of Φ are derived.

Keywords

RANDOM SURFACEGAUSS'DIVERGENCE THEOREMSTOCHASTIC GEOMETRYRANDOM MEASUREPALM PROBABILITYCONSERVATION LAWLINEAR CONTACT DISTRIBUTIONPOINT PROCESS

MSC classification

Primary: 60G57: Random measures
Secondary: 60D05: Geometric probability and stochastic geometry

Information

Type
Stochastic Geometry amd Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 13 - 28
Copyright
Copyright © Applied Probability Trust 1996 

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