scholarly journals Introducing a Stationary Skew-Gaussian Random Field

2022 ◽  
Vol 15 (2) ◽  
pp. 549-566
Author(s):  
Omid Karimi ◽  
Fatemeh Hosseini ◽  
◽  
Keyword(s):  
Random Field ◽  
Gaussian Random Field

scholarly journals ULTRAMETRIC RANDOM FIELD

2006 ◽  
Vol 09 (02) ◽  
pp. 199-213 ◽  
Author(s):  
A. YU. KHRENNIKOV ◽  
S. V. KOZYREV
Keyword(s):  
Wavelet Analysis ◽  
Random Field ◽  
Stochastic Equation ◽  
Gaussian Random Field ◽  
Ultrametric Space ◽  
Ultrametric Spaces

Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion of ultrametric Markovianity, which describes independence of contributions to random field from different ultrametric balls is introduced. We show that the random field under investigation satisfies this property.

scholarly journals The Transparent Dead Leaves Model

2012 ◽  
Vol 44 (01) ◽  
pp. 1-20 ◽  
Author(s):  
B. Galerne ◽  
Y. Gousseau
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Field ◽  
Central Limit ◽  
Gaussian Random Field ◽  
Natural Images ◽  
Simulation Algorithm ◽  
New Model ◽  
Grain Model ◽  
Dead Leaves Model

In this paper we introduce the transparent dead leaves (TDL) random field, a new germ-grain model in which the grains are combined according to a transparency principle. Informally, this model may be seen as the superposition of infinitely many semitransparent objects. It is therefore of interest in view of the modeling of natural images. Properties of this new model are established and a simulation algorithm is proposed. The main contribution of the paper is to establish a central limit theorem, showing that, when varying the transparency of the grain from opacity to total transparency, the TDL model ranges from the dead leaves model to a Gaussian random field.

Temporally Consistent Gaussian Random Field for Video Semantic Analysis

2007 ◽  
Author(s):  
Jinhui Tang ◽  
Xian-Sheng Hua ◽  
Tao Mei ◽  
Guo-Jun Qi ◽  
Shipeng Li ◽  
...  
Keyword(s):  
Random Field ◽  
Semantic Analysis ◽  
Gaussian Random Field ◽  
Video Semantic Analysis

scholarly journals THE TOPOLOGY OF THE COSMIC MICROWAVE BACKGROUND ANISOTROPY ON THE SCALE ~1°

1996 ◽  
Vol 05 (04) ◽  
pp. 319-362 ◽  
Author(s):  
D.I. NOVIKOV ◽  
H.E. JØRGENSEN
Keyword(s):  
Cosmic Microwave Background ◽  
Random Field ◽  
Gaussian Noise ◽  
Gaussian Random Field ◽  
Cosmological Models ◽  
Topological Method ◽  
Microwave Background ◽  
Cosmic Microwave Background Anisotropy ◽  
Non Gaussian

In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky maps based on these results. We have simulated 10°×10° sky maps of the cosmic microwave background anisotropy expected from different cosmological models with 0.5°–1° resolution in order to demonstrate how this method can be used for detection of non-Gaussian noise in the maps and detection of the Doppler-peak in the spectrum of perturbation of ΔT/T.

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