Issues

 / 

1989

 / 

May

  

Reviews of topical problems


Randomness, determinateness, and predictability


Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation

The basic conventions regarding randomness employed in mathematics (set-theoretical approach, algorithmic approach) and in physics (decaying correlations, continuous spectrum, hyperbolicity, fractal nature, uncontrollability, nonrepeatability, nonreproducibility, nonpredictability, etc.) are analyzed. It is pointed out that phenomena that are random from one viewpoint may be determinate from another viewpoint. The concept of partially determinate processes, i.e., processes that admit prediction over bounded time intervals, is discussed. The theory of partially determinate processes is based on identifying randomness with unpredictability and establishes the interrelation between the real physical process $x(t)$, the observed process $y(t)$, and the model (predictive, hypothetical) process $t(t)$. In this theory the degree of determinateness, which is denned as the correlation coefficient between the observed process and prediction, is employed as a measure of the quality of predictability. Diverse theoretical, experimental, and numerical measures of partially determinate processes as well as examples of partially determinate fields are presented. It is emphasized that the time of determinate (i.e., predictable) behavior $\tau_{\det}$ of an observed process $y(t)$ can be much longer than the correlation time $\tau_c$, and the degree of coherence is the worst estimate of the degree of determinateness. From the viewpoint expounded determinate chaos stands out as a completely determinate process over short time intervals ($\tau\ll\tau_{\det}$), as a completely random process over long intervals ($\tau\gg\tau_{\det}$), and as a partially determinate process over intermediate time intervals $\tau\sim\tau_{\det}$. It is significant that in the interval between $\tau_c$ and $\tau_{\det}$ chaotic and turbulent fields admit both a determinate and statistical (kinetic) description.

Fulltext pdf (768 KB)
Fulltext is also available at DOI: 10.1070/PU1989v032n05ABEH002718
PACS: 05.40.−a, 05.45.Ac (all)
DOI: 10.1070/PU1989v032n05ABEH002718
URL: https://ufn.ru/en/articles/1989/5/c/
Citation: Kravtsov Yu A "Randomness, determinateness, and predictability" Sov. Phys. Usp. 32 434–449 (1989)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Кравцов Ю А «Случайность, детерминированность, предсказуемость» УФН 158 93–122 (1989); DOI: 10.3367/UFNr.0158.198905c.0093

Cited by (36) ↓ Similar articles (20)

  1. Proskuryakov A Y, Kropotov Y A Procedia Engineering 201 789 (2017)
  2. Medvinsky A B, Nurieva N I et al BIOPHYSICS 62 92 (2017)
  3. Makarenko A V IFAC-PapersOnLine 48 1049 (2015)
  4. Norman G E, Stegailov V V Math Models Comput Simul 5 305 (2013)
  5. Mushailov B R, Teplitskaya V S Cosmic Res 51 362 (2013)
  6. Kostenko P Yu, Simonenko S N i dr Izvestiya Vuzov. Radioelektronika 55 3 (2012)
  7. Kostenko P Yu, Symonenko S N et al Radioelectron.Commun.Syst. 55 475 (2012)
  8. Bunich A L Autom Remote Control 72 2351 (2011)
  9. Terebizh V Yu Bull.Crim. Astrophys. Observ. 106 103 (2010)
  10. Berczyñski S, Kravtsov Yu A, Anosov O Chaos, Solitons & Fractals 41 1459 (2009)
  11. ANOSOV O, HENSEL B et al Int. J. Bifurcation Chaos 17 1661 (2007)
  12. Butkovskiĭ O Ya, Logunov M Yu J. Exp. Theor. Phys. 104 966 (2007)
  13. Moiseev S N Optoelectron.Instrument.Proc. 43 400 (2007)
  14. Ivanov L M, Margolina T M, Danilov A I Journal Of Marine Systems 48 117 (2004)
  15. Morozov I V, Norman G E J. Phys. A: Math. Gen. 36 6005 (2003)
  16. Morozov I V, Norman G E, Valuev A A Phys. Rev. E 63 (3) (2001)
  17. Ivanov L M, Kirwan A D, Margolina T M Journal Of Marine Systems 28 113 (2001)
  18. Norman G E, Stegailov V V J. Exp. Theor. Phys. 92 879 (2001)
  19. Rajan S D, Doutt J A, Carey W M IEEE J. Oceanic Eng. 23 174 (1998)
  20. Srinivasan, R S, Wood, Kristin L 1 199 (1998)
  21. Anosov O L, Butkovskii O Ya, Kravtsov Yu A Springer Series In Synergetics Vol. Predictability of Complex Dynamical SystemsStrategy and Algorithms for Dynamical Forecasting69 Chapter 6 (1996) p. 105
  22. Anosov O L, Butkovskii O Ya Springer Series In Synergetics Vol. Predictability of Complex Dynamical SystemsA Discriminant Procedure for the Solution of Inverse Problems for Nonstationary Systems69 Chapter 4 (1996) p. 67
  23. Moiseev N N Springer Series In Synergetics Vol. Predictability of Complex Dynamical SystemsLimits of Predictability for Biospheric Processes69 Chapter 10 (1996) p. 169
  24. Kadtke Ja B, Kravtsov Yu A Springer Series In Synergetics Vol. Predictability of Complex Dynamical SystemsIntroduction69 Chapter 1 (1996) p. 3
  25. Vassiliadis D, Klimas A J et al J. Geophys. Res. 100 3495 (1995)
  26. Eremeev V N, Ivanov L M et al Journal Of Environmental Radioactivity 27 49 (1995)
  27. Monin A S, Piterbarg L I Springer Series In Synergetics Vol. Limits of PredictabilityForecasting Weather and Climate60 Chapter 2 (1993) p. 7
  28. Malinetskii G G Springer Series In Synergetics Vol. Limits of PredictabilitySynergetics, Predictability and Deterministic Chaos60 Chapter 4 (1993) p. 75
  29. Sadovskii M A, Pisarenko V F Springer Series In Synergetics Vol. Limits of PredictabilityPrediction of Time Series60 Chapter 6 (1993) p. 161
  30. Kontor N N Advances In Space Research 13 417 (1993)
  31. Kravtsov Yu A Springer Series In Synergetics Vol. Limits of PredictabilityFundamental and Practical Limits of Predictability60 Chapter 7 (1993) p. 173
  32. Borovik A S, Kovaleva E A, Malyshevski V S Radiation Effects And Defects In Solids 125 119 (1993)
  33. Grandy W T Found Phys 22 853 (1992)
  34. Eremeev V N, Ivanov L M, Kirwan A D J. Geophys. Res. 97 9733 (1992)
  35. Kravtsov Y A Rep. Prog. Phys. 55 39 (1992)
  36. Kravtsov Yu A Radiophys Quantum Electron 33 242 (1990)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions