Statistically instable processes: connection with flicker, nonequilibrium, fractal and colored noise
DOI:
https://doi.org/10.3103/S0735272712030016Keywords:
flicker noise, nonequilibrium noise, statistically instable process, fractal process, theory of hyper-random phenomenaAbstract
Analytical expressions that link statistical instability parameters with process’s spectrum are obtained. It is shown that statistical stability is determined solely by the character of spectral power density dependence on frequency. It is revealed that statistically stable noises are those with rising intensity when frequency is increased, white noise, and equilibrium flicker noise described by the dependence 1/f β where the spectrum shape parameter is 0 < β < 1 as well as fractal Gaussian noise. Statistically instable noises are nonequilibrium flicker noises with spectral power density 1/f β when β >= 1. It is determined that not only random nonstationary and deterministic processes are statistically instable as it was considered earlier, but stationary processes as well.
References
I. I. Gorban, Theory of Hyper-Random Phenomena (IPMMS NANU, Kyiv, 2007) [in Russian], http://ifsc.ualr.edu/jdberleant/intprob/.
I. I. Gorban, Theory of Hyper-Random Phenomena: Physical and Mathematical Basics (Naukova Dumka, Kyiv, 2011) [in Russian], http://
www.immsp.kiev.ua/perspages/gorban_i_i/index.html.
I. I. Gorban, “Disturbance of statistical stability,” Information Models of Knowledge (ITHEA, Sofia, 2010), pp. 398–410.
А. N. Shiriayev, Basics of Stochastic Financial Mathematics, Vol. 1: Facts, Models (FAZIS, Moscow, 1998) [in Russain].
I. I. Gorban, “Statistical Instability of Physical Processes,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 54 (9), 40 (2011) [Radioelectron. Commun. Syst. 54 (9), 499 (2011)], DOI: 10.3103/S0735272711090044.
W. Schottky, Phys. Rev. 28, 74 (1926).
J. B. Johnson, Phys. Rev. 26, 71 (1925).
Sh. M. Cogan, “Low-frequnecy current noise with spectrum of kind 1/f in solid bodies,” Physics – Uspekhi 145, No. 2, 285 (1985).
G. P. Zhigal’skiy, “Nonequilibrium 1/f g noise in conducting films and connectors,” Physics – Uspekhi 173, No. 5, 465 (2003).
Yu. L. Klimontovich, Introduction to Physics of Open Systems (Yanus-K, Moscow, 2002) [in Russian].
R. F. С. Vеssоt, “Course 56,” in Experimental Gravitation : Proc. of Int. School of Physics “Enrico Fermi” (Academic Press, New York, 1974), p. 111.
J. J. Gagnepain and J. Uebersfeld, in Proc. of Symp. on 1/f Fluctuations (Tokyo, 1977) [ed. by T. Musha], p. 173.
R. М. Crownover, Introduction to Fractals and Chaos (Jones & Bartlett, Boston, 1995).
Y. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes (Springer-Verlag, Berlin–Heidelberg, 2008).
G. W. Wornell, “Fractal Signals,” in Digital Signal Processing (CRC Press LLC, Boca Raton, 1999) [ed. by V. K. Madisetti and D. B. Williams].
