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2 results

Anisotropic scaling of the random grain model with application to network traffic
Part of
- Stochastic processes
- Special processes
Vytautė Pilipauskaitė, Donatas Surgailis
Journal:

Journal of Applied Probability / Volume 53 / Issue 3 / September 2016

Published online by Cambridge University Press:

24 October 2016, pp. 857-879

Print publication:

September 2016
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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.

The fractional mixed fractional brownian motionand fractional brownian sheet
Charles El-Nouty
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

17 August 2007, pp. 448-465

Print publication:

June 2007
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 We introduce the fractional mixed fractional Brownian motion and fractionalBrownian sheet, and investigate the small ball behavior of its sup-norm statistic.Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.

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2 results

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

The fractional mixed fractional brownian motionand fractional brownian sheet