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Shot noise on cluster processes with cluster marks, and studies of long range dependence

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Filemon Ramirez-Perez  and
Robert Serfling
Filemon Ramirez-Perez*
Affiliation:
Universidad Autonoma Chapingo
Robert Serfling*
Affiliation:
University of Texas at Dallas
*
∗ Postal address: Area de Estadistica, Departamento de Fitotecnia, Universidad Autonoma Chapingo, Chapingo Edo. Mex. CP56230, Mexico.
∗∗ Postal address: Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75083-0688, USA. Email address: serfling@utdallas.edu
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Abstract

With the aim of providing greater flexibility in developing and applying shot noise models, this paper studies shot noise on cluster point processes with both pointwise and cluster marks. For example, in financial modelling, responses to events in the financial market may occur in clusters, with random amplitudes including a ‘cluster component’ reflecting a degree of commonness among responses within a cluster. For such shot noise models, general formulae for the characteristic functional are developed and specialized to the case of Neyman-Scott clustering with cluster marks. For several general forms of response function, long range dependence of the corresponding equilibrium shot noise models is investigated. It is shown, for example, that long range dependence holds when the ‘structure component’ of the response function decays slowly enough, or when the response function has a finite random duration with a heavy tailed distribution.

Keywords

Shot noisepoint processescluster processeslong range dependenceheavy tailsequilibrium behaviourfinancial modelling

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 60G35: Signal detection and filtering
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 631 - 651
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

Supported by NSF Grants DMS-9705209 and DMS-0103698.

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