2006, Vol.9, No.4, pp.313-330

In this paper we develop the new approach in time series analysis with a variable time step and present the results of quantitative and qualitative estimation of randomness and regularity, and the study of non-Markovian effects of the X-ray emission intensity of the microquasar GRS 1915+105. Our estimation is based on the application of the theory of discrete non-Markovian stochastic processes and gives a wide set of quantitative characteristics and parameters of the studied system with a variable time step. This set reflects the change of the effects of randomness and regularity, the alternation of Markovian and non-Markovian processes in the initial time signals. Initially these characteristics were determined for the simple model systems constructed by means of a molecular dynamics method. Further the calculation of these parameters was executed for the X-ray emission intensity of the microquasar GRS 1915+105. We have developed a theoretical scheme for the detailed analysis of the time series with a variable time step. The new theory allows us to extract more detailed information about the X-ray emission of the microquasar GRS 1915+105 from the experimental time series. The received set of the parameters allows to estimate accurately randomness and stochastic behavior, regularity and robustness, non-Markovian effects of statistical memory in the intensity of the X-ray emission. The analysis of the experimental data with a constant and variable time step is carried out by means of phase portraits, power spectra of the initial time and event correlation function (TCF and ECF), and memory functions (MF) of the junior order, the first three points of non-Markovity parameter.
Key words: discrete non-Markov processes, time series analysis, randomness and non-Markovity, X-ray intensity of GRS 1915+105

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