Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study
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 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.
Cite
@article{arxiv.1611.07386,
title = {Generalized Radon--Nikodym Spectral Approach. Application to Relaxation Dynamics Study},
author = {Aleksandr Vasilievich Bobyl and Andrei Georgievich Zabrodskii and Mikhail Evgenievich Kompan and Vladislav Gennadievich Malyshkin and Olga Valentinovna Novikova and Ekaterina Evgenievna Terukova and Dmitry Valentinovich Agafonov},
journal= {arXiv preprint arXiv:1611.07386},
year = {2018}
}
Comments
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