Stochastic Differential Equations and Processes

Volume 7 of the series Springer Proceedings in Mathematics pp 151-178


General Shot Noise Processes and Functional Convergence to Stable Processes

  • Wissem JedidiAffiliated withDepartment of Mathematics, Faculty of Sciences of Tunis Email author 
  • , Jalel AlmhanaAffiliated withGRETI group, University of Moncton
  • , Vartan ChoulakianAffiliated withGRETI group, University of Moncton
  • , Robert McGormanAffiliated withNORTEL Networks

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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.