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Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study

Authors :
Bobyl, Aleksandr Vasilievich
Zabrodskii, Andrei Georgievich
Kompan, Mikhail Evgenievich
Malyshkin, Vladislav Gennadievich
Novikova, Olga Valentinovna
Terukova, Ekaterina Evgenievna
Agafonov, Dmitry Valentinovich
Publication Year :
2016

Abstract

Radon--Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with $L^2$ norm approaches, such as Fourier or least squares, this new approach does not use a norm, the problem is reduced to finding the spectrum of an operator (virtual Hamiltonian), which is built in a way that eigenvalues represent the dynamic characteristic of interest and eigenvectors represent probability density. The problems of interpolation (numerical estimation of Radon--Nikodym derivatives is developed) and obtaining the distribution of relaxation rates from sampled timeserie are considered. Application of the theory is demonstrated on a number of model and experimentally measured timeserie signals of degradation and relaxation processes. Software product, implementing the theory is developed.<br />Comment: Grammar fixes. Relation to Global Optimization added. Software description update. For the processes with infinite second or third moment, added: an example of skewness estimator, and an example of "a replacement to standard deviation" as max \lambda - min \lambda, that is finite even for the processes with infinite second moment. Lebesgue integral quadrature relation added

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1611.07386
Document Type :
Working Paper