Negligent killing of scientific concepts: the stationarity case;Meurtre par imprudence de concepts scientifiques: le cas de la stationnarité

Hydrological Sciences Journal

Volumn 60, Issue 7-8, 2015, Pages 1174-1183

  Koutsoyiannis, Demetris ^a   Montanari, Alberto ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

change; Panta Rhei; stationarity; stochastics

Indexed keywords

STOCHASTIC SYSTEMS;

NON-STATIONARITIES; STATIONARITY; STATIONARY PROCESS;

STOCHASTIC MODELS;

CONCEPTUAL FRAMEWORK; FUTURE PROSPECT; NUMERICAL MODEL; PHILOSOPHY; STOCHASTICITY;

EID: 84940609858     PISSN: 02626667     EISSN: 21503435     Source Type: Journal    
DOI: 10.1080/02626667.2014.959959     Document Type: Article

References (22)

1. M.L.Bachelier,, 1900. Théorie de la spéculation. Annales scientifiques de l'École Normale Supérieure, 17, 21–86.
2. G.D.Birkhoff,, 1931. Proof of the ergodic theorem. Proceedings of the National Academy of Sciences, 17, 656–660. doi:10.1073/pnas.17.12.656
3. Commission for Hydrology, 2013. CHy Statement on the Terms Stationarity and Nonstationarity, World Meteorological Organization. Available from: http://www.wmo.int/pages/prog/hwrp/publications/statements/Stationarity_CHy_Statement.pdf.
4. B.P.Conrad,, 2003. Differential equations, a systems approach. Upper Saddle River, NJ: Prentice Hall, 462 pp.
5. J.L.Doob,, 1934. Stochastic processes and statistics. Proceedings of the National Academy of Sciences of the United States of America, 20 (6), 376–379. doi:10.1073/pnas.20.6.376
6. H.Georgiou, and M.D.Sharma,, 2012. University students’ understanding of thermal physics in everyday contexts. International Journal of Science and Mathematics Education, 10, 1119–1142. doi:10.1007/s10763-011-9320-1
7. M.G.Kendall, and A.Stuart,, 1966. The advanced theory of statistics, vol. 3: design and analysis, and time-series. London: Griffin, 552 pp.
8. A.Khintchine,, 1934. Korrelationstheorie der stationären stochastischen Prozesse. Mathematische Annalen, 109 (1), 604–615. doi:10.1007/BF01449156
9. A.N.Kolmogorov,, 1931. Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Mathematische Annalen, 104, 415–458. (English translation: On analytical methods in probability theory, In: Kolmogorov, A.N., 1992. Selected Works of A. N. Kolmogorov - Volume 2, Probability Theory and Mathematical Statistics A. N. Shiryayev, ed., Kluwer, Dordrecht, The Netherlands, pp. 62–108) doi:10.1007/BF01457949
10. A.N.Kolmogorov,, 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung (Ergebnisse der Mathematik und Ihrer Grenzgebiete), Berlin (2nd English Edition: Foundations of the Theory of Probability, 84 pp. Chelsea Publishing Company, New York, 1956).
11. A.N.Kolmogorov,, 1938. A simplified proof of the Birkhoff-Khinchin ergodic theorem. Uspekhi Matematicheskikh Nauk, 5, 52–56. (English edition: Kolmogorov, A.N., 1991, Selected Works of A. N. Kolmogorov - Volume 1, Mathematics and Mechanics, Tikhomirov, V. M. ed., Kluwer, Dordrecht, The Netherlands, pp. 271–276)
12. A.N.Kolmogorov,, 1947. Statistical theory of oscillations with continuous spectrum, Collected papers on the 30th anniversary of the Great October Socialist Revolution, Vol. 1, Akad. Nauk SSSR, Moscow-Leningrad, pp. 242–252. (English edition: Kolmogorov, A.N., 1992. Selected Works of A. N. Kolmogorov - Volume 2, Probability Theory and Mathematical Statistics A. N. Shiryayev ed., Kluwer, Dordrecht, The Netherlands, pp. 321–330).
13. D.Koutsoyiannis,, 2010. A random walk on water. Hydrology and Earth System Sciences, 14, 585–601. doi:10.5194/hess-14-585-2010
14. D.Koutsoyiannis,, 2011. Hurst-Kolmogorov dynamics and uncertainty. JAWRA Journal of the American Water Resources Association, 47 (3), 481–495. doi:10.1111/j.1752-1688.2011.00543.x
15. A.Lasota, and M.C.Mackey,, 1994. Chaos, fractals and noise. New York: Springer-Verlag.
16. M.C.Mackey,, 1992. Time’s arrow: the origins of thermodynamic behavior. Mineola, NY: Dover, 175 pp.
17. P.C.D.Milly,, et al., 2008. Climate change: stationarity is dead: whither water management? Science, 319, 573–574. doi:10.1126/science.1151915
18. A.Montanari,, et al., 2013. “Panta Rhei—Everything Flows”: change in hydrology and society—The IAHS Scientific Decade 2013–2022. Hydrological Sciences Journal, 58 (6), 1256–1275. doi:10.1080/02626667.2013.809088
19. A.Montanari, and D.Koutsoyiannis,, 2012. A blueprint for process-based modeling of uncertain hydrological systems. Water Resources Research, 48, W09555. doi:10.1029/2011WR011412
20. A.Papoulis,, 1991. Probability, random variables, and stochastic processes. 3rd ed. New York: McGraw-Hill.
21. E.Parzen,, 1957. On consistent estimates of the spectrum of a stationary time series. The Annals of Mathematical Statistics, 28 (2), 329–348. doi:10.1214/aoms/1177706962
22. S.Wiggins,, 2003. Introduction to applied nonlinear dynamical systems and chaos. 2nd ed. New York: Springer-Verlag, 843 pp.