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Analytic properties and covariance functions for a new class of generalized gibbs random fields

D.T. Hristopulo, S. Elogne

Απλή Εγγραφή


URIhttp://purl.tuc.gr/dl/dias/7CDE17A9-1EEE-4546-8E0C-D098037807A0-
Αναγνωριστικόhttps://doi.org/10.1109/TIT.2007.909163-
Γλώσσαen-
Μέγεθος12 pagesen
ΤίτλοςAnalytic properties and covariance functions for a new class of generalized gibbs random fieldsen
ΔημιουργόςD.T. Hristopuloen
ΔημιουργόςS. Elogneen
ΕκδότηςIEEEen
ΠερίληψηSpartan spatial random fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions and a small set of free parameters (interaction couplings). This paper focuses on the fluctuation-gradient-curvature (FGC) SSRF model, henceforth referred to as FGC-SSRF. This model is defined on the Euclidean space R by means of interactions proportional to the squares of the field realizations, as well as their gradient and curvature. The permissibility criteria of FGC-SSRFs are extended by considering the impact of a finite-bandwidth kernel. It is proved that the FGC-SSRFs are almost surely differentiable in the case of finite bandwidth. Asymptotic explicit expressions for the Spartan covariance function are derived for d = 1 and d= 3; both known and new covariance functions are obtained depending on the value of the FGC-SSRF shape parameter. Nonlinear dependence of the covariance integral scale on the FGC-SSRF characteristic length is established, and it is shown that the relation becomes linear asymptotically. The results presented in this paper are useful in random field parameter inference, and in spatial interpolation of irregularly spaced samples.en
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2015-09-25-
Ημερομηνία Δημοσίευσης2007-
Θεματική ΚατηγορίαGreek mathematicsen
Θεματική Κατηγορίαmathematics greeken
Θεματική Κατηγορίαgreek mathematicsen
Βιβλιογραφική ΑναφοράD.T. Hristopulos , S. Elogne ," Analytic properties and covariance functions for a new class of generalized Gibbs random fields" , IEEE Tran. on Inf. Th.,vol. 53 ,no. 12, pp.4667-4679,2007f. doi : 10.1109/TIT.2007.909163en

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