Modeling Dynamical Behavior of Stochastic Systems: Spectral Analysis of Qubit Representations vs the Mutual Markovian Model Likelihood Estimations

Abstract

The formal quantum systems under study demonstrate significant capabilities for solving classification problems in studying dynamical behavior of stochastic systems. Among their features are entanglement by measuring, quantitative estimating the fit for a closed qubit system and observations to identify qubit representation parameters, the specialized discretized spectral metric for comparing patterns of system behaviors, with the multidimensional scaling, cluster analysis and discriminant analysis being applied to the matrices of mutual distances calculated using the presented discretized spectral metric. Hidden evolution periodicities during the observation time period are determined by means of the quantum systems spectral analysis to clarify the system behavior structure. These systems can be also used for representing the Markovian processes with the aid of qubit representations of staying in the corresponding states. An illustrative example revealed diagnostic benefits of the new technique as compared with one based on the Markovian representation.