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Anisotropic scaling of the random grain model with application to network traffic

Published online by Cambridge University Press:  24 October 2016

Vytautė Pilipauskaitė*
Affiliation:
Université de Nantes and Vilnius University
Donatas Surgailis*
Affiliation:
Vilnius University
*
* Postal address: Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania.
* Postal address: Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania.

Abstract

We obtain a complete description of anisotropic scaling limits of the random grain model on the plane with heavy-tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both coordinate axes and include stable, Gaussian, and ‘intermediate’ infinitely divisible random fields. The asymptotic form of the covariance function of the random grain model is obtained. Application to superimposed network traffic is included.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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