Asymptotic mean stationarity of sources with finite evolution dimension

IEEE Transactions on Information Theory

Volumn 53, Issue 7, 2007, Pages 2342-2348

  Faigle, Ulrich ^a   Schönhuth, Alexander ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Asymptotic mean; Dimension; Entropy; Ergodic; Evolution operator; Hidden Markov model (HMM); Linearly dependent process; Markov chain; Observable operator model; Random source; Stable; State generating function; Stationary

Indexed keywords

EVOLUTION OPERATOR; LINEARLY DEPENDENT PROCESS; OBSERVABLE OPERATOR MODEL; STATE GENERATING FUNCTION;

DYNAMICAL SYSTEMS; MARKOV PROCESSES; RANDOM PROCESSES;

ASYMPTOTIC ANALYSIS;

EID: 34447302314     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.899514     Document Type: Article

References (15)

1. S. P. M. Choi, D.-Y. Yeung, and N. L. Zhang, "Hidden-Markov decision processes for nonstationary sequential decision making," in Sequence Learning (Lecture Notes in Artificial Intelligence), R. Sun and C. L. Giles, Eds. Berlin, Germany: Springer-Verlag, 2000, vol. 1828, pp. 264-287.
2. T. S. Han and K. Kobayashi, in Mathematics of Information and Coding Providence, R.I., 2002, vol. 203, Amer. Math. Soc. Mathematical Monographs.
3. R. M. Gray and J. C. Kieffer, "Asymptotically mean stationary measures," Ann. Probab., vol. 8, pp. 962-973, 1980.
4. A. Heller, "On stochastic processes derived from Markov chains," Ann. Math. Statist., vol. 36, pp. 1286-1291, 1965.
5. H. Ito, S.-I. Amari, and K. Kobayashi, "Identifiability of hidden Markov information sources and their minimum degrees of freedom," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 324-333, Mar. 1992.
6. E. J. Gilbert, "On the identifiability problem for functions of finite Markov chains," Ann. Math. Statist., vol. 30, pp. 688-697, 1959.
7. A. Heller, "Probabilistic automata and stochastic transformations," Math. Syst. Theory, vol. 1, no. 3, pp. 197-208, 1967.
8. H. Jaeger, "Observable operator models for discrete stochastic time series," Neural Comput., vol. 12, pp. 1371-1398, 2000.
9. J. C. Kieffer and M. Rahe, "Markov channels are asymptotically mean stationary," SIAM J. Math. Anal., vol. 12, no. 3, pp. 293-305, 1981.
10. R. K. Brayton and C. H. Tong, "Stability of dynamical systems: A constructive approach," IEEE Trans. Circuits Syst., vol. CAS-26, no. 4, pp. 224-234, Apr. 1979.
11. A. Schönhuth, "Diskrete Stochastische Vektorräume," Ph.D. dissertation, Univ. Cologne, Cologne, Germany, 2006.
12. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," in Proc. 33rd ACM Symp. theory of Computing (STOC , New York, 2001, pp. 50-59.
13. U. Faigle and A. Schönhuth, "Quantum predictor models," Electon. Notes Discr. Math., vol. 25, pp. 149-155, 2006.
14. S. D. Jacka and G. O. Roberts, "On strong forms of weak convergence," Stochastic Processes and Applications, vol. 67, pp. 41-53, 1997.
15. R. J. Elliot, L. Aggoun, and J. B. Moore, Hidden Markov Models. Heidelberg, Germany: Springer-Verlag, 1995.