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Perturbation analysis of functionals of random measures

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

François Baccelli ,
Maurice Klein  and
Sergei Zuyev
François Baccelli*
Affiliation:
INRIA, Sophia-Antipolis
Maurice Klein*
Affiliation:
CNET, Issy Les Moulineaux
Sergei Zuyev*
Affiliation:
INRIA, Sophia Antipolis
*
* Postal address: INRIA, Centre de Sophia Antipolis, 2004 Route des Lucioles, 06565 Valbonne Cedex, France.
** Postal address: CNET, 38 Rue du Général Leclerc, 92131 Issy les Moulineaux, France.
* Postal address: INRIA, Centre de Sophia Antipolis, 2004 Route des Lucioles, 06565 Valbonne Cedex, France.
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Abstract

We use the fact that the Palm measure of a stationary random measure is invariant to phase space change to generalize the light traffic formula initially obtained for stationary processes on a line to general spaces. This formula gives a first-order expansion for the expectation of a functional of the random measure when its intensity vanishes. This generalization leads to new algorithms for estimating gradients of functionals of geometrical random processes.

Keywords

STATIONARY RANDOM MEASURESSTATIONARY POINT PROCESSESPALM MEASURECAMPBELL MEASURELIGHT TRAFFIC ANALYSISPERTURBATION ANALYSISGRADIENT ESTIMATES IN COMPUTER SIMULATIONSSTOCHASTIC GEOMETRYVORONOI CELL

MSC classification

Primary: 60G55: Point processes
Secondary: 60G57: Random measures 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 306 - 325
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Mendendez Pelayo, Valencia, Spain, on 21–24 September 1993.

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