Effectiveness of statistically optimal estimate of Hurst's indicator of generalized fractal Gaussian process distorted by white noise

Kostiantyn S. Vasiuta; A. V. Shapovalov; V. I. Storogev

doi:10.3103/S0735272710090062

Authors

Kostiantyn S. Vasiuta Ivan Kozhedub Kharkiv National Air Force University, Ukraine https://orcid.org/0000-0002-1978-3717
A. V. Shapovalov Kharkiv Air Force University, Ukraine
V. I. Storogev Kharkiv Air Force University, Ukraine

DOI:

https://doi.org/10.3103/S0735272710090062

Keywords:

Hurst' indicator, optimum estimation, white noise, generalized fractal Gaussian process, potential accuracy

Abstract

In the article the maximum likelihood estimate of Hurst's indicator for a generalized fractal Gaussian process observed at the background of white Gaussian noise in considered. Potential estimate's accuracy and its dependence on inessential observation parameters: spectral density of fractal process and noise, and on the samples number in the observation spectrum.

References

О. I. Shelukhin, А. М. Tenyakshiyev, and A. V. Osin, Fractal Processes in Telecommunications (Radiotekhnika, Moscow, 2003) [in Russian].
J. Feder, Fractal (Plenum Press, New York, 1988; Mir, Moscow, 1991).
S. Ye. Fal’kovich and P. Yu. Kostenko, Statistical Theory of Radio Engineering Systems (NAU KhAI, Kharkov, 2005) [in Russian].