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May 2014 Perturbation analysis of Poisson processes
Günter Last
Bernoulli 20(2): 486-513 (May 2014). DOI: 10.3150/12-BEJ494

Abstract

We consider a Poisson process $\Phi$ on a general phase space. The expectation of a function of $\Phi$ can be considered as a functional of the intensity measure $\lambda$ of $\Phi$. Extending earlier results of Molchanov and Zuyev [Math. Oper. Res. 25 (2010) 485–508] on finite Poisson processes, we study the behaviour of this functional under signed (possibly infinite) perturbations of $\lambda$. In particular, we obtain general Margulis–Russo type formulas for the derivative with respect to non-linear transformations of the intensity measure depending on some parameter. As an application, we study the behaviour of expectations of functions of multivariate Lévy processes under perturbations of the Lévy measure. A key ingredient of our approach is the explicit Fock space representation obtained in Last and Penrose [Probab. Theory Related Fields 150 (2011) 663–690].

Citation

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Günter Last. "Perturbation analysis of Poisson processes." Bernoulli 20 (2) 486 - 513, May 2014. https://doi.org/10.3150/12-BEJ494

Information

Published: May 2014
First available in Project Euclid: 28 February 2014

zbMATH: 1303.60039
MathSciNet: MR3178507
Digital Object Identifier: 10.3150/12-BEJ494

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 2 • May 2014
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