Probabilistic analysis of two-dimensional vector random processes on the phase plane
Vitaly Ivanovich Khimenko · Информационно-управляющие системы · 2019
Introduction: The models of vector random processes are characterized by a variety of practical applications and, at the same time, by the complexity of studying the detailed probabilistic structure. Such features often lead to considering only separate components of vector functions, forcing the shift to scalar process analysis. All this significantly reduces the overall information content of the research, increasing the relevance of the search for promising approaches to probabilistic analysis of vector processes. Purpose: To present vector random processes in a phase space of states, and to apply the general theory of level crossings of random functions to the study of probabilistic structure of phase trajectories. Results: We have identified the characteristic features of displaying randomprocesses on a phase plane, and introduced numerical characteristics for the description and analysis of probabilistic behavior of samplefunctions. A probabilistic analysis has been performed for the characteristics of the «level crossing» type for vector processes withvarious definitions of the areas of acceptable values. We used the typical models of two-dimensional Gaussian processes and «signalplus noise» models to demonstrate how the probabilistic structure of the phase trajectories depends on the given threshold levels, majordistribution parameters and spectral-correlation properties of the studied processes. Practical relevance: The article contributes tothe research information content and its visualization in the analysis of probabilistic behavior of vector random processes. It combinesgeneral methods of phase space of vector processes, methods of phase plane in the analysis of scalar processes and the theory of levelcrossings of random functions. The classical approaches to the visual description of phase trajectories are supplemented by the methodsof quantitative analysis of detailed probabilistic structure of random functions.