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General Shot Noise Processes and Functional Convergence to Stable Processes

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Stochastic Differential Equations and Processes

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 7))

Abstract

In traffic modeling theory, many authors present models based on particular shot noise representations. We propose here a model based on a general Poisson shot noise representation. Under minimal assumptions, we obtain an approximation of the cumulative input process by a stable Lévy motion via a functional limit theorem.

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Acknowledgements

The authors would like to thank the referees for pointing out the obscure 635 points and for their helpful comments, which improved the presentation of this paper. This work 636 was funded by Atlantic Canada Opportunity Agency (ACOA) and through grant from the National 637 Science and Engineering Research Council of Canada (NSERC) to Dr. Vartan Choulakian.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, Campus Universitaire, 1060, Tunis, Tunisia

    Wissem Jedidi

  2. GRETI group, University of Moncton, Moncton, NB E1A3E9, Canada

    Jalel Almhana & Vartan Choulakian

  3. NORTEL Networks, 4001 E. Chapel Hill-Nelson Hwy, research Triangle Park, Durham, North Carolina, USA, 27709

    Robert McGorman

Authors
  1. Wissem Jedidi
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  2. Jalel Almhana
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  3. Vartan Choulakian
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  4. Robert McGorman
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Corresponding author

Correspondence to Wissem Jedidi .

Editor information

Editors and Affiliations

  1. to the Military Academies, Department of Mathematics, Preparatory Institute, Avenue Marechal Tito, Sousse, 4029, Tunisia

    Mounir Zili

  2. Jan Kochanowski University in Kielce, ul. Krakowska 11, Kielce, 25-029, Poland

    Darya V. Filatova

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© 2012 Springer-Verlag Berlin Heidelberg

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Jedidi, W., Almhana, J., Choulakian, V., McGorman, R. (2012). General Shot Noise Processes and Functional Convergence to Stable Processes. In: Zili, M., Filatova, D. (eds) Stochastic Differential Equations and Processes. Springer Proceedings in Mathematics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22368-6_3

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