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Analyticity of Poisson-driven stochastic systems

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Michael A. Zazanis
Michael A. Zazanis*
Affiliation:
Northwestern University
*
∗Postal address: Northwestern University, Department of Industrial Engineering and Management Sciences, 2145 Sheridan Rd, Evanston, IL 60208, USA.
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Abstract

Let ψ be a functional of the sample path of a stochastic system driven by a Poisson process with rate λ . It is shown in a very general setting that the expectation of ψ,Eλ [ψ], is an analytic function of λ under certain moment conditions. Instead of following the straightforward approach of proving that derivatives of arbitrary order exist and that the Taylor series converges to the correct value, a novel approach consisting in a change of measure argument in conjunction with absolute monotonicity is used. Functionals of non-homogeneous Poisson processes and Wiener processes are also considered and applications to light traffic derivatives are briefly discussed.

Keywords

POISSON PROCESSESANALYTIC FUNCTIONSABSOLUTELY MONOTONIC FUNCTIONSQUEUEING SYSTEMSLIGHT TRAFFIC DERIVATIVES

MSC classification

Primary: 60G55: Point processes
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 532 - 541
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by NSF Grants ECS-8811003 and DDM-8905638.

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