General Shot Noise Processes and Functional Convergence to Stable Processes

  • Wissem Jedidi
  • Jalel Almhana
  • Vartan Choulakian
  • Robert McGorman
Conference paper

DOI: 10.1007/978-3-642-22368-6_3

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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wissem Jedidi
    • 1
  • Jalel Almhana
    • 2
  • Vartan Choulakian
    • 2
  • Robert McGorman
    • 3
  1. 1.Department of MathematicsFaculty of Sciences of TunisTunisTunisia
  2. 2.GRETI groupUniversity of MonctonMonctonCanada
  3. 3.NORTEL NetworksDurhamUSA

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