Testing nonlinear Markovian hypotheses in dynamical systems

Physica D: Nonlinear Phenomena

Volumn 104, Issue 1, 1997, Pages 61-74

  Schittenkopf, Christian ^a,b   Deco, Gustavo ^a  

^a SIEMENS AG   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Information flow; Markov process; Surrogate method

Indexed keywords

APPROXIMATION THEORY; CALCULATIONS; CHAOS THEORY; ITERATIVE METHODS; MARKOV PROCESSES; MATHEMATICAL MODELS; REGRESSION ANALYSIS; SPURIOUS SIGNAL NOISE;

HIGHER ORDER CUMULANTS; INFORMATION FLOW; SURROGATE METHOD; THEILER METHOD;

INFORMATION THEORY;

EID: 0031143561     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00230-8     Document Type: Article

References (37)

1. R. Shaw, Z. Naturforsch. A 36 (1981) 80.
2. J.D. Farmer, Z. Naturforsch. A 37 (1982) 1304.
3. J.P. Crutchfield and N.H. Packard, Physica D 7 (1983) 201.
4. K. Matsumoto and I. Tsuda, J. Phys. A 18 (1985) 3561.
5. R.W. Leven and B. Pompe, Ann. Phys. 43 (1986) 259.
6. B. Pompe, J. Kruscha and R.W. Leven, Z. Naturforsch. A 41 (1986) 801.
7. A.M. Fraser, IEEE Trans. Inform. Theory 35 (1989) 245.
8. G. Györgyi and P. Szépfalusy, Phys. Rev. A 31 (1985) 3477.
9. P. Szépfalusy and G. Györgyi, Phys. Rev. A 33 (1986) 2852.
10. J.P. Eckmann and D. Ruelle, Rev. Modern Phys. 57 (1985) 617.
11. A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 119 (1958) 861.
12. A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 124 (1959) 754.
13. Y.G. Sinai, Dokl. Akad. Nauk SSSR 124 (1959) 768.
14. Y.G. Sinai, Dokl. Akad. Nauk SSSR 125 (1959) 1200.
15. A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Physica D 16 (1985) 285.
16. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50 (1983) 346.
17. R.W. Leven, B.P. Koch and B. Pompe, Chaos in Dissipativen Systemen (Akademie-Verlag, Berlin, 1994).
18. G. Deco, C. Schittenkopf and B. Schürmann, Int. J. Bifur. Chaos, in press.
19. C. Schittenkopf and G. Deco, Physica D 94 (1996) 57.
20. G. Deco and B. Schürmann, Phys. Rev. E 51 (1995) 1780.
21. G. Deco and B. Schürmann, Phys. Rev. E 52 (1995) 6580.
22. G. Deco and D. Obradovic, An Information Theoretic Approach to Neural Computing (Springer, New York, 1995).
23. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J.D. Farmer, Physica D 58 (1992) 77.
24. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, Singapore, 1991).
25. C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1990).
26. L. Breiman, Statistics: With a View Toward Applications (Houghton Mifflin, Boston, MA, 1973).
27. A.M. Albano, P.E. Rapp and A. Passamante, Phys. Rev. E 52 (1995) 196.
28. B.W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman & Hall, London, 1986).
29. M. Rosenblatt, Ann. Math. Statist. 27 (1956) 832.
30. E. Parzen, Ann. Math. Statist. 33 (1962) 1065.
31. R. Neuneier, W. Finnoff, F. Hergert and D. Ormoneit, Estimation of conditional densities: A comparison of neural network approaches. in: Int. Conf. on Artificial Neural Networks, ICANN (Springer, Berlin, 1994) p. 689.
32. C.M. Bishop, Technical Report, Aston University, Birmingham, UK (1994).
33. C.M. Bishop, Neural Networks for Pattern Recognition (Clarendon Press, Oxford, 1995).
34. E.N. Lorenz, J. Atmospheric Sci. 20 (1963) 130.
35. G.U. Yule, Philos. Trans. Roy. Soc. London A 226 (1927) 267.
36. H. Tong, Non-linear Time Series: A Dynamical System Approach (Oxford University Press, Oxford, 1990).
37. M. Casdagli, J. Roy. Statist. Soc. B 54 (1991) 303.