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

2016 ◽  
Vol 53 (3) ◽  
pp. 857-879 ◽  
Author(s):  
Vytautė Pilipauskaitė ◽  
Donatas Surgailis
Keyword(s):  
Network Traffic ◽  
Random Fields ◽  
Covariance Function ◽  
Asymptotic Form ◽  
Scaling Limits ◽  
Infinitely Divisible ◽  
Area Distribution ◽  
Anisotropic Scaling ◽  
Grain Model ◽  
Heavy Tailed

AbstractWe 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.

scholarly journals Scaling limits for a random boxes model

2019 ◽  
Vol 51 (03) ◽  
pp. 773-801
Author(s):  
F. Aurzada ◽  
S. Schwinn
Keyword(s):  
Random Fields ◽  
Random Measure ◽  
Statistical Properties ◽  
Scaling Limits ◽  
Poisson Random Measure ◽  
Scaling Behaviour ◽  
The Mean ◽  
Heavy Tailed

AbstractWe consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e. independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are heavy tailed with different parameters. We investigate the scaling behaviour of the related random fields as the intensity of the random measure grows to infinity while the mean edge lengths tend to zero. We characterise the arising scaling regimes, identify the limiting random fields, and give statistical properties of these limits.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

scholarly journals Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

2017 ◽  
Vol 54 (3) ◽  
pp. 833-851 ◽  
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Random Field ◽  
Large Class ◽  
Random Fields ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Excursion Sets ◽  
Excursion Set ◽  
Fixed Radius ◽  
Asymptotic Probability ◽  
The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

scholarly journals Highly Anisotropic Scaling Limits

2015 ◽  
Vol 162 (4) ◽  
pp. 997-1030 ◽  
Author(s):  
M. Cassandro ◽  
M. Colangeli ◽  
E. Presutti
Keyword(s):  
Scaling Limits ◽  
Anisotropic Scaling
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