Anisotropic scaling limits of long-range dependent random fields

2019 ◽  
Vol 59 (4) ◽  
pp. 595-615 ◽  
Author(s):  
Donatas Surgailis
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Scaling Limits ◽  
Anisotropic Scaling

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 random fields with long-range dependence

2007 ◽  
Vol 35 (2) ◽  
pp. 528-550 ◽  
Author(s):  
Ingemar Kaj ◽  
Lasse Leskelä ◽  
Ilkka Norros ◽  
Volker Schmidt
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Long Range Dependence ◽  
Scaling Limits

Long-range Terrain Perception Based on Conditional Random Fields

ROBOT ◽  
2010 ◽  
Vol 32 (3) ◽  
pp. 326-333
Author(s):  
Mingjun WANG ◽  
Jun ZHOU ◽  
Jun TU ◽  
Chengliang LIU
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Conditional Random Fields

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

scholarly journals Limiting crossing probabilities of random fields

2006 ◽  
Vol 43 (03) ◽  
pp. 884-891 ◽  
Author(s):  
L. Pereira ◽  
H. Ferreira
Keyword(s):  
General Theory ◽  
Long Range ◽  
Random Fields ◽  
Extremal Index ◽  
Weak Dependence ◽  
Local Path ◽  
Crossing Probabilities

Random fields on , with long-range weak dependence for each coordinate individually, usually present clustering of high values. For each one of the eight directions in , we formulate restriction conditions on local occurrence of two or more crossings of high levels. These smooth oscillation conditions enable computation of the extremal index as a clustering measure from the limiting mean number of crossings. In fact, only four directions must be inspected since for opposite directions we find the same local path crossing behaviour and the same limiting mean number of crossings. The general theory is illustrated with several 1-dependent nonstationary random fields.

scholarly journals Generalised spectral analysis of fractional random fields

1997 ◽  
Vol 62 (1) ◽  
pp. 64-83
Author(s):  
V. V. Anh ◽  
K. E. Lunney
Keyword(s):  
Spectral Analysis ◽  
Spectral Density ◽  
Long Range ◽  
Random Fields ◽  
Spectral Decomposition ◽  
Covariance Function ◽  
Long Range Dependence ◽  
Type Condition ◽  
Fractal Index ◽  
Fractal Characteristics

AbstractThis paper considers a large class of non-stationary random fields which have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the spectral domain.The paper develops a spectral theory for the random fields, including a spectral decomposition, a covariance representation and a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These concepts are useful in multiscaling analysis of random fields with long-range dependence.

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