The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. M BARNSLEY, S. DEMKO, J. ELTON and J. GERINOMO (1988). Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Ann. Inst. Henri Poincaré, Prob. Statist. , 24:367--394. Erratum (1989) Ann. Inst. H. PoincarÈ Probab. Statist. 25:589--590. MR 89k:60088
  2. H. BERBEE (1987). Chains with infinite connections: Uniqueness and Markov representation. Probab. Th. Rel. Fields , 76:243--253. MR 89c:60052
  3. R. BOWEN (1975). Equilibrium states and the ergodic theory of Anosov diffeomorphisms , Lecture Notes in Mathematics, volume 470. Springer. MR 56:1364
  4. X. BRESSAUD, R. FERNANDEZ, and A. GALVES (1998). Speed of $overline{d}$-convergence for Markov approximations of chains with complete connections. A coupling approach. Preprint. To be published in Stoch. Proc. and Appl.
  5. Z. COELHO and A. N. QUAS (1998). Criteria for $overline d$-continuity. Trans. Amer. Math. Soc. , 350:3257--3268. Math. Review number not available.
  6. K. BURDZY and W. KENDALL (1998). Efficient Markovian couplings: examples and counterexamples. Preprint. Math. Review number not available.
  7. W. DOEBLIN (1938). Exposé sur la théorie des chaînes simples constantes de Markoff à un nombre fini d'états. Rev. Math. Union Interbalkanique , 2:77--105. Math. Review number not available.
  8. W. DOEBLIN (1940). Remarques sur la théorie métrique des fractions continues. Composition Math. , 7:353--371. MR 2,107e
  9. W. DOEBLIN and R. FORTET (1937). Sur les chaînes à liaisons complétes. Bull. Soc. Math. France , 65:132--148. Math. Review number not available.
  10. T. E. HARRIS (1955). On chains of infinite order. Pacific J. Math. , 5:707--724. MR 17,755b
  11. M. IOSIFESCU (1978). Recent advances in the metric theory of continued fractions. Trans. 8th Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978) , Vol. A, pp. 27--40, Reidel, Dordrecht-Boston, Mass. MR 80h:10059
  12. M. IOSIFESCU (1992). A coupling method in the theory of dependence with complete connections according to Doeblin. Rev. Roum. Math. Pures et Appl. , 37:59--65. MR 94b:60120
  13. M. IOSIFESCU and S. GRIGORESCU (1990). Dependence with Complete Connections and its Applications , Cambridge University Press, Cambridge. MR 91j:60098
  14. M. IOSIFESCU and R. THEODORESCU (1969). Random Processes and Learning , Springer-Verlag, Berlin. MR 45:2781
  15. T. KAIJSER (1981). On a new contraction condition for random systems with complete connections. Rev. Roum. Math. Pures et Appl. , 26:1075--1117. MR 83e:60101b
  16. T. KAIJSER (1994). On a theorem of Karlin. Acta Applicandae Mathematicae , 34:51--69. MR 95h:60101
  17. S. KARLIN (1953). Some random walks arising in learning models. J. Pacific Math. , 3:725--756. MR 15,450a
  18. A. KONDAH, V. MAUME and B. SCHMITT (1996). Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non Höldériennes. Technical Report 88, Université de Bourgogne. Math. Review number not available.
  19. S. P. LALLEY (1986). Regeneration representation for one-dimensional Gibbs states. Ann. Prob. , 14:1262--1271. MR 88c:60076
  20. F. LEDRAPPIER (1974). Principe variationnel et systémes dynamiques symboliques. Z. Wahrscheinlichkeitstheorie verw. Gebiete , 30:185--202. MR 53:8384
  21. T. LINDVALL (1991). W. Doeblin 1915--1940. Ann. Prob. , 19:929--934. MR 92k:01036
  22. T. LINDVALL (1992). Lectures on the Coupling Method , Wiley, New York. MR 94c:60002
  23. C. LIVERANI (1995). Decay of correlations. Ann. of Math. , 142(2):239--301. MR 96e:58090
  24. F. NORMAN (1972). Markov Processes and Learning Models , Academic Press, New York. MR 54:11522
  25. O. ONICESCU and G. MIHOC (1935). Sur les chaînes statistiques. C. R. Acad. Sci. Paris , 200:5121---512. Math. Review number not available.
  26. O. ONICESCU and G. MIHOC (1935a). Sur les chaînes de variables statistiques. Bull. Sci., Math. , 59:174--192. Math. Review number not available.
  27. W. PARRY and M. POLLICOTT (1990). Zeta functions and the periodic structure of hyperbolic dynamics. Asterisque 187-188. MR 92f:58141
  28. M. POLLICOTT (1997). Rates of mixing for potentials of summable variation. Preprint.
  29. A. N. QUAS (1996). Non-ergodicity for C¹ expanding maps and g-measures. Ergod. Th. Dynam. Sys. , 16:531--543. MR 97d:28025
  30. D. RUELLE (1978). Thermodynamic formalism . Encyclopedia of Mathematics and its applications, volume 5. Addison-Wesley, Reading, Massachusetts. MR 80g:82017
  31. P. WALTERS (1975). Ruelle's operator theorem and g-measures. Trans. Amer. Math. Soc. , 214:375--387. MR 54:515
  32. P. WALTERS (1978). Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. , 236:121--153. MR 57:6371
  33. L.-S. YOUNG (1997). Recurrence times and rates of mixing. Preprint. Math. Review number not available.
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.