Some remarks on the purely nondeterministic property of second order random fields

2005 ◽  
pp. 98-109
Author(s):  
G. Kallianpur
Keyword(s):  
Random Fields ◽  
Second Order

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

On stationarity and second-order properties of bilinear random fields

2014 ◽  
Vol 17 (3) ◽  
pp. 221-244
Author(s):  
Abdelouahab Bibi ◽  
Karima Kimouche
Keyword(s):  
Random Fields ◽  
Second Order

scholarly journals Stein's method for negatively associated random variables with applications to second-order stationary random fields

2018 ◽  
Vol 55 (1) ◽  
pp. 196-215 ◽  
Author(s):  
Nathakhun Wiroonsri
Keyword(s):  
Normal Distribution ◽  
Random Vector ◽  
Random Fields ◽  
Second Order ◽  
Multidimensional Case ◽  
Standard Normal Distribution ◽  
Smooth Functions ◽  
Negatively Associated ◽  
Standard Normal ◽  
Stationary Random Fields

Abstract Let ξ = (ξ1, . . ., ξm) be a negatively associated mean-zero random vector with components that obey the bound |ξi| ≤ B, i = 1, . . ., m, and whose sum W = ∑i=1mξi has variance 1. The bound d1(ℒ(W), ℒ(Z)) ≤ 5B - 5.2∑i≠ jσij is obtained, where Z has the standard normal distribution and d1(∙, ∙) is the L1 metric. The result is extended to the multidimensional case with the L1 metric replaced by a smooth functions metric. Applications to second-order stationary random fields with exponential decreasing covariance are also presented.

scholarly journals Covariance function and ergodicity of asymptotically stationary random fields

1991 ◽  
Vol 44 (1) ◽  
pp. 49-62 ◽  
Author(s):  
V.V. Anh ◽  
K.E. Lunney
Keyword(s):  
Ergodic Theorem ◽  
Random Fields ◽  
Covariance Function ◽  
Spectral Representation ◽  
Second Order ◽  
Continuity Theorem ◽  
Mean Ergodic Theorem ◽  
Stationary Random Fields

A class of second-order asymptotically stationary random fields is shown to contain the class of almost harmonisable random fields. A continuity theorem which leads to the spectral representation for the covariance function of asymptotically stationary random fields is established. A mean ergodic theorem for the fields is also given. When stationarity is assumed, the results reduce to the well-known corresponding theorems for stationary random fields.

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