An Interdisciplinary Journal

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

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.

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Last updated: *July 16, 2002*