Anisotropic scaling of the random grain model with application to network traffic
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This article is published in Journal of Applied Probability.The article was published on 2016-09-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Scaling.read more
Citations
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Scaling transition for nonlinear random fields with long-range dependence
TL;DR: In this article, a complete description of anisotropic scaling limits and the existence of scaling transition for nonlinear functions (Appell polynomials) of stationary linear random fields on Z 2 with moving average coefficients decaying at possibly different rate in the horizontal and the vertical direction are given.
Journal ArticleDOI
Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance
TL;DR: In this paper, the joint temporal and contemporaneous aggregation of N independent copies of random-coefficient AR(1) processes driven by independent and identically distributed innovations in the domain of normal attraction of an -stable distribution is discussed.
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Anisotropic scaling limits of long-range dependent linear random fields on Z3
TL;DR: In this article, the authors provided a complete description of anisotropic scaling limits of stationary linear random field (RF) on Z 3 with long-range dependence and moving average coefficients decaying as O( | t i | − q i ) in the ith direction, i = 1, 2, 3.
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Anisotropic scaling limits of long-range dependent random fields
TL;DR: In this paper, the scaling transition for linear and their subordinated nonlinear long-range dependent stationary random fields X on ℤ2 has been studied and the scaling limits are taken over rectangles in Ω2 whose sides increase as O(λ) and O (λγ ) as λ→∞ for any fixed γ > 0.
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Scaling transition and edge effects for negatively dependent linear random fields on Z2
TL;DR: In this article, a complete description of anisotropic scaling limits and the existence of scaling transition for a class of negatively dependent linear random fields X on Z 2 with moving-average coefficients a ( t, s ) decaying as | t | − q 1 and | s| − q 2 in the horizontal and vertical directions, q 1 − 1 + q 2 − 1 1 1 and satisfying ∑ ( t, s ) ∈ Z 2 a (t, s) = 0.
References
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Journal ArticleDOI
Non-central limit theorems for non-linear functional of Gaussian fields
R. L. Dobrushin,Péter Major +1 more
TL;DR: In this article, the authors studied the limit behavior as N→∞ and showed that the norming constants tend to infinity more rapidly than the usual norming sequence when the correlation function r(n) tends slowly to 0, and generalized the results to the case when the parameter set is multi-dimensional.
Journal ArticleDOI
Central limit theorems for non-linear functionals of Gaussian fields
Péter Breuer,Péter Major +1 more
TL;DR: In this article, it was shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero.
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Is network traffic approximated by stable Levy motion or fractional Brownian motion
TL;DR: In this article, the authors show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable Levy motion is a sensible approximation to cumulative traffic over a time period.
Journal ArticleDOI
Operator scaling stable random fields
TL;DR: In this paper, the authors present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing E -homogeneous functions φ, satisfying φ ( c E x ) = c φ( x ).
Journal ArticleDOI
Zones of attraction of self-similar multiple integrals
TL;DR: In this article, Surgailis et al. considered the multidimensional case of convergence to self-similar fields and gave a short survey of the separate sections of the paper, including the connection of this theorem with the result of Dobrushin-Major [8] and some similar questions.
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