Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.2, pp.129-136

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.2, pp.129-136

Statistical Theory of Non-Stationary Time Correlation in Complex Systems with Discrete Time.
Renat Yulmetyev, Peter Hänggi, and Fail Gafarov

We develop the statistical theory of discrete non-stationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of non-stationarity effects. The developed theory starts from careful analysis of time correlation through non-stationary dynamics of vectors of initial and final states and non-stationary normalized TCF. Using of projection operators technique we find the chain of finite-difference non-Markov kinetic equations for discrete non-stationary TCF and for the set of non-stationary discrete memory functions (MF). The last contains supplementary information about non-stationary properties of complex system in a whole. Another relevant result of our theory is a construction of a set of dynamic parameters of non-stationarity, which contains information on non-stationarity effects. The full set of dynamic parameters and kinetic functions ( TCF, short MF, statistical spectra of non-Markovity parameter and statistical spectra of non-stationarity parameter) has made possible in-depth information about discreteness, non-Markov effects, long-range memory and non-stationarity of underlying processes.
Key words: non-Markov discrete processes, non-stationary time correlation, finite-discrete kinetic equations, memory functions.

Full text: Acrobat PDF (135KB) PostScript (489KB) PostScript.gz (138KB)