| Title:
|
On the concept of the asymptotic Rényi distances for random fields (English) |
| Author:
|
Janžura, Martin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
[353]-366 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| MSC:
|
60G60 |
| MSC:
|
60K35 |
| MSC:
|
62B10 |
| MSC:
|
62M40 |
| MSC:
|
82B05 |
| idZBL:
|
Zbl 1274.62061 |
| idMR:
|
MR1704671 |
| . |
| Date available:
|
2009-09-24T19:26:16Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135292 |
| . |
| Reference:
|
[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, MR 0219345 |
| Reference:
|
[2] Georgii H. O.: Gibbs Measures and Place Transitions.de Gruyter, Berlin 1988 MR 0956646 |
| Reference:
|
[3] Liese F., Vajda I.: Convex Statistical Problems.Teubner, Leipzig 1987 MR 0926905 |
| Reference:
|
[4] Perez A.: Risk estimates in terms of generalized $f$–entropies.In: Proc. Colloq. Inform. Theory (A. Rényi, ed.), Budapest 1968 MR 0263542 |
| Reference:
|
[5] Rényi A.: On measure of entropy and information.In: Proc. 4th Berkeley Symp. Math. Statist. Probab., Univ. of Calif. Press, Berkeley 1961, Vol. 1, pp. 547–561 MR 0132570 |
| Reference:
|
[6] Vajda I.: On the $f$–divergence and singularity of probability measures.Period. Math. Hungar. 2 (1972), 223–234 Zbl 0248.62001, MR 0335163, 10.1007/BF02018663 |
| Reference:
|
[7] Vajda I.: The Theory of Statistical Inference and Information.Kluwer, Dordrecht – Boston – London 1989 |
| . |
