Janžura, Martin On the concept of the asymptotic Rényi distances for random fields. (English) Zbl 1274.62061 Kybernetika 35, No. 3, 353-366 (1999). Summary: The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions. Cited in 1 ReviewCited in 2 Documents MSC: 62B10 Statistical aspects of information-theoretic topics 62M40 Random fields; image analysis PDF BibTeX XML Cite \textit{M. Janžura}, Kybernetika 35, No. 3, 353--366 (1999; Zbl 1274.62061) Full Text: Link References: [1] Csiszár I.: Information-type measures of difference of probability distributions and indirect observations. Stud. Sci. Math. Hungar. 2 (1967), 299-318 · Zbl 0157.25802 [2] Georgii H. O.: Gibbs Measures and Place Transitions. de Gruyter, Berlin 1988 [3] Liese F., Vajda I.: Convex Statistical Problems. Teubner, Leipzig 1987 · Zbl 0656.62004 [4] Perez A.: Risk estimates in terms of generalized \(f\)-entropies. Proc. Colloq. Inform. Theory (A. Rényi, Budapest 1968 · Zbl 0184.43303 [5] Rényi A.: On measure of entropy and information. Proc. 4th Berkeley Symp. Math. Statist. Probab., Univ. of Calif. Press, Berkeley 1961, Vol. 1, pp. 547-561 [6] Vajda I.: On the \(f\)-divergence and singularity of probability measures. Period. Math. Hungar. 2 (1972), 223-234 · Zbl 0248.62001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.