Small and Large Scale Behavior of the Poissonized Telecom Process

Serge Cohen () and Murad S. Taqqu ()
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Serge Cohen: Université Paul Sabatier
Murad S. Taqqu: Boston University

Methodology and Computing in Applied Probability, 2004, vol. 6, issue 4, 363-379

Abstract: Abstract The stable Telecom process has infinite variance and appears as a limit of renormalized renewal reward processes. We study its Poissonized version where the infinite variance stable measure is replaced by a Poisson point measure. We show that this Poissonized version converges to the stable Telecom process at small scales and to the Gaussian fractional Brownian motion at large scales. This process is therefore locally as well as asymptotically self-similar. The value of the self-similarity parameter at large scales, namely the self-similarity parameter of the limit fractional Brownian motion, depends on the form the Poissonized Telecom process. The Poissonized Telecom process is a Poissonized mixed moving average. We investigate more general Poissonized mixed moving averages as well.

Keywords: fractional Brownian motion; self-similarity; local self-similarity; Telecom process (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/B:MCAP.0000045085.17224.82

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