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Monte Carlo methods for sensitivity analysis of Poisson-driven stochastic systems, and applications

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Charles Bordenave  and
Giovanni Luca Torrisi
Charles Bordenave*
Affiliation:
University of California, Berkeley
Giovanni Luca Torrisi*
Affiliation:
Istituto per le Applicazioni del Calcolo ‘Mauro Picone’
*
∗ Postal address: Department of Electrical Engineering and Computer Science and Department of Statistics, University of California, 257 Cory Hall, Berkeley, CA 94720-1770, USA.
∗∗ Postal address: Istituto per le Applicazioni del Calcolo ‘Mauro Picone’, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italy. Email address: torrisi@iac.rm.cnr.it
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Abstract

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We extend a result due to Zazanis (1992) on the analyticity of the expectation of suitable functionals of homogeneous Poisson processes with respect to the intensity of the process. As our main result, we provide Monte Carlo estimators for the derivatives. We apply our results to stochastic models which are of interest in stochastic geometry and insurance.

Keywords

Importance samplingmarked Poisson processMonte Carlo estimatorsensitivity analysisstabilizing functionalstopping set

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 65C05: Monte Carlo methods
Secondary: 60G48: Generalizations of martingales 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 293 - 320
Copyright
Copyright © Applied Probability Trust 2008 

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