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Nonstationary covariance functions that model space–time interactions

✍ Scribed by Chunsheng Ma

Book ID
104302045
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
149 KB
Volume
61
Category
Article
ISSN
0167-7152

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✦ Synopsis

This paper shows how to derive nonstationary spatio-temporal covariance functions via spatio-temporal stationary covariances and intrinsically stationary variograms. Three closely related kernels are employed for this purpose:

(i) 2{'(s 1 ; t 1 ) + '(s 2 ; t 2 )} -'(s 1 + s 2 ; t 1 + t 2 ) -'(s 1 -s 2 ; t 1 -t 2 ), (ii) '(s 1 + s 2 ; t 1 + t 2 ) -'(s 1 -s 2 ; t 1 -t 2 ), (iii) '(s 1 ; t 1 ) + '(s 2 ; t 2 ) -'(s 1 -s 2 ; t 1 -t 2 ), where '(s; t) is an intrinsically stationary variogram. Typical examples of covariances generated by kernel (iii) are those of the Brownian motion and fractional Brownian motion. Many new nonseparable spatio-temporal covariance functions are obtained via kernels (i) and (ii).

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