On reconstruction of the Ito-like equation from persistent time series

• Autorzy: Czechowski Z.

Identyfikatory

DOI

10.2478/s11600-013-0117-1

• Języki publikacji: EN

Abstrakty

EN

The Langevin equation with finite-range persistence was introduced as a macroscopic model of various geophysical phenomena. The modified histogram procedure (MHP) of reconstruction of the equation from time series was proposed. An efficiency of MHP was tested on artificial persistent time series (with short and long-tail distributions) generated by different Ito-like equations. For an exemplary geophysical time series, the appropriate Ito-like equation was reconstructed.

Słowa kluczowe

EN

stochastic process; nonlinear time series modeling; persistence; Ito equation; Fokker-Planck equation

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2013
• Tom: Vol. 61, no. 6
• Strony: 1504--1521
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Czechowski Z.

• Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland

Bibliografia

• 1. Białecki, M. (2012a), Motzkin numbers out of Random Domino Automaton, Phys. Lett. A 376,45, 3098-3100, DOI: 10.1016/j.physleta.2012.09.022.
• 2. Białecki, M. (2012b), An explanation of the shape of the universal curve of the Scaling Law for the Earthquake Recurrence Time Distributions, arXiv:1210.7142 [physics.geo-ph].
• 3. Białecki, M., and Z. Czechowski (2010), On a simple stochastic cellular automaton with avalanches: simulation and analytical results. In: V. de Rubeis, Z. Czechowski, and R. Teisseyre (eds.), Synchronization and Triggering: from Fracture to Earthquake Processes, GeoPlanet - Earth and Planetary Sciences, Vol. 1, Springer, Berlin Heidelberg, 63-75, DOI: 10.1007/978-3-642-12300-9_5.
• 4. Białecki, M., and Z. Czechowski (2013), On one-to-one dependence of rebound parameters on statistics of clusters: exponential and inverse-power distributions out of Random Domino Automaton, J. Phys. Soc. Jpn. 82, 014003, DOI: 10.7566/JPSJ.82.014003.
• 5. Box, G.E.P., and G.M. Jenkins (1970), Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco.
• 6. Brockwell, P.J., and R.A. Davis (1987), Time Series: Theory and Methods, Springer, New York.
• 7. Czechowski, Z. (1991), A kinetic model of crack fusion, Geophys. J. Int. 104,2, 419-422, DOI: 10.1111/j.1365-246X.1991.tb02521.x.
• 8. Czechowski, Z. (1993), A kinetic model of nucleation, propagation and fusion of cracks, J. Phys. Earth 41,3, 127-137, DOI: 10.4294/jpe1952.41.127.
• 9. Czechowski, Z. (2001), Transformation of random distributions into power-like distributions due to non-linearities: application to geophysical phenomena, Geophys. J. Int. 144,1, 197-205, DOI: 10.1046/j.1365-246x.2001.00318.x.
• 10. Czechowski, Z. (2003), The privilege as the cause of power distributions in geophysics, Geophys. J. Int. 154,3, 754-766, DOI: 10.1046/j.1365-246X.2003.01994.x.
• 11. Czechowski, Z. (2005), The importance of the privilege in resource redistribution models for appearance of inverse-power solutions, Physica A 345,1-2, 92-106, DOI: 10.1016/j.physa.2004.07.014.
• 12. Czechowski, Z. (2010), The importance of privilege for the appearance of long-tail distributions. In: V. de Rubeis, Z. Czechowski, and R. Teisseyre (eds.), Synchronization and Triggering: from Fracture to Earthquake Processes, GeoPlanet - Earth and Planetary Sciences, Vol. 1, Springer, Berlin Heidelberg, 97-119, DOI: 10.1007/978-3-642-12300-9_7.
• 13. Czechowski, Z., and M. Białecki (2010), Ito equations as macroscopic stochastic models of geophysical phenomena - construction of the models on the basis of time series. In: V. de Rubeis, Z. Czechowski, and R. Teisseyre (eds.), Synchronization and Triggering: from Fracture to Earthquake Processes, GeoPlanet: Earth and Planetary Sciences, Vol. 1, Springer, Berlin Heidelberg, 77-96, DOI: 10.1007/978-3-642-12300-9_6.
• 14. Czechowski, Z., and M. Białecki (2012a), Ito equations out of domino cellular automaton with efficiency parameters, Acta Geophys. 60,3, 846-857, DOI: 10.2478/s11600-012-0021-0.
• 15. Czechowski, Z., and M. Białecki (2012b), Three-level description of the domino cellular automaton, J. Phys. A 45,15, 155101, DOI: 10.1088/1751-8113/45/15/155101.
• 16. Czechowski, Z., and A. Rozmarynowska (2008), The importance of the privilege for appearance of inverse-power solutions in Ito equations, Physica A 387,22, 5403-5416, DOI: 10.1016/j.physa.2008.06.007.
• 17. Czechowski, Z., and L. Telesca (2011), The construction of an Ito model for geoelectrical signals, Physica A 390,13, 2511-2519, DOI: 10.1016/j.physa.2011.02.049.
• 18. Gardiner, C.W. (1985), Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, Springer, Berlin.
• 19. Grasman, J., and O.A. van Herwaarden (1999), Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications, Springer, Berlin Heidelberg, DOI: 10.1007/978-3-662-03857-4.
• 20. Kantelhardt, J.W., E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, and A. Bunde (2001), Detecting long-range correlations with detrended fluctuation analysis, Physica A 295,3-4, 441-454, DOI: 10.1016/S0378-4371(01)00144-3.
• 21. Mandelbrot, B.B., and J.W. Van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10,4, 422-437, DOI: 10.1137/1010093.
• 22. Øksendal, B. (1998), Stochastic Differential Equations: An Introduction with Applications, 5th ed., Springer, Berlin Heidelberg, 324 pp.
• 23. Risken, H. (1996), The Fokker-Planck Equation. Methods of Solution and Applications, 3rd ed., Springer, Berlin Heidelberg.
• 24. Rozmarynowska, A. (2009), On the reconstruction of Ito models on the basis of time series with long-tail distributions, Acta Geophys. 57,2, 311-329, DOI: 10.2478/s11600-008-0074-2.
• 25. Siegert, S., R. Friedrich, and J. Peinke (1998), Analysis of data sets of stochastic systems, Phys. Lett. A 243,5-6, 275-280, DOI: 10.1016/S0375-9601(98)00283-7.
• 26. Telesca, L., and Z. Czechowski (2012), Discriminating geoelectrical signals measured in seismic and aseismic areas by using Ito models, Physica A 391,3, 809-818, DOI: 10.1016/j.physa.2011.09.006.
• 27. Tsallis, C. (2012), Nonadditive entropy Sq and nonextensive statistical mechanics: applications in geophysics and elsewhere, Acta Geophys. 60,3, 502-525, DOI: 10.2478/s11600-012-0005-0.