Strictly positive definite correlation functions

2006 ◽  
Author(s):  
John Dolloff ◽  
Brian Lofy ◽  
Alan Sussman ◽  
Charles Taylor
Keyword(s):  
Correlation Functions ◽  
Positive Definite ◽  
Definite Correlation

scholarly journals Positive Definite Norm Dependent Matrices In Stochastic Modeling

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Sebastian P. Kuniewski ◽  
Jolanta K. Misiewicz
Keyword(s):  
Stochastic Modeling ◽  
Mathematical Analysis ◽  
Spatial Data ◽  
Correlation Matrix ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Necessary Condition ◽  
The Family ◽  
Definite Correlation

AbstractPositive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial data. Because the positive definiteness is a necessary condition for a matrix to be a valid correlation matrix, it is desirable to give a characterization of the family of the distance/norm dependent functions that form a valid (positive definite) correlation matrix. Thus, the main reason for writing this paper is to give an overview of characterizations of norm dependent real functions and consequently norm dependent matrices, since this information is somehow hidden in the theory of geometry of Banach spaces

Isotropic correlation functions on d-dimensional balls

1999 ◽  
Vol 31 (03) ◽  
pp. 625-631
Author(s):  
Tilmann Gneiting
Keyword(s):  
Data Analysis ◽  
Spatial Data ◽  
Correlation Functions ◽  
Dimensional Space ◽  
Extension Theorem ◽  
Spatial Dimension ◽  
Positive Definite ◽  
Spatial Data Analysis ◽  
Spatial Lag ◽  
Image Position

A popular procedure in spatial data analysis is to fit a line segment of the formc(x) = 1 - α ||x||, ||x|| < 1, to observed correlations at (appropriately scaled) spatial lagxind-dimensional space. We show that such an approach is permissible if and only ifthe upper bound depending on the spatial dimensiond. The proof relies on Matheron's turning bands operator and an extension theorem for positive definite functions due to Rudin. Side results and examples include a general discussion of isotropic correlation functions defined ond-dimensional balls.

Stabilität von Vielteilchensystemen bei äußeren Störungen:

1966 ◽  
Vol 21 (10) ◽  
pp. 1556-1561 ◽  
Author(s):  
Richard Lenk
Keyword(s):  
Correlation Functions ◽  
Physical Meaning ◽  
Linear Response ◽  
Second Law Of Thermodynamics ◽  
Positive Definite ◽  
Second Law ◽  
Response Functions ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

As a consequence of the Second Law of Thermodynamics the imaginary parts of linear response functions are positive definite for positive frequencies. Resulting from this fact inequalities based on the fluctuation dissipation theorem are derived for the moments of these imaginary parts and of the related correlation functions. Moments without physical meaning have been eliminated.

Isotropic correlation functions on d-dimensional balls

1999 ◽  
Vol 31 (3) ◽  
pp. 625-631 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Data Analysis ◽  
Spatial Data ◽  
Correlation Functions ◽  
Dimensional Space ◽  
Extension Theorem ◽  
Spatial Dimension ◽  
Positive Definite ◽  
Spatial Data Analysis ◽  
Spatial Lag ◽  
Image Position

A popular procedure in spatial data analysis is to fit a line segment of the form c(x) = 1 - α ||x||, ||x|| < 1, to observed correlations at (appropriately scaled) spatial lag x in d-dimensional space. We show that such an approach is permissible if and only if the upper bound depending on the spatial dimension d. The proof relies on Matheron's turning bands operator and an extension theorem for positive definite functions due to Rudin. Side results and examples include a general discussion of isotropic correlation functions defined on d-dimensional balls.

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