Karachanskaya, Elena Random harmonic processes with new properties. (English) Zbl 1483.60055 Karapetyants, Alexey N. (ed.) et al., Operator theory and harmonic analysis. OTHA 2020, Part II – probability-analytical models, methods and applications. Based on the international conference on modern methods, problems and applications of operator theory and harmonic analysis. Cham: Springer. Springer Proc. Math. Stat. 358, 243-252 (2021). Summary: In this paper, we introduce a new general model for random signals and adjoining harmonic processes. This model is stochastic hierarchically correlated series (SHCS). The sufficient conditions for both the wide-sense stationary property and the mean ergodic property for random harmonic (trigonometric) processes are set. Moreover, we describe a class of wide-sense stationary and mean ergodic random harmonic processes function with nonuniformly random phase.For the entire collection see [Zbl 1470.46003]. MSC: 60G10 Stationary stochastic processes 62M15 Inference from stochastic processes and spectral analysis Keywords:stochastic hierarchically correlated series; wide-sense stationarity; mean ergodicity; nonuniformly random phase PDFBibTeX XMLCite \textit{E. Karachanskaya}, Springer Proc. Math. Stat. 358, 243--252 (2021; Zbl 1483.60055) Full Text: DOI References: [1] Antipenskiy, R.: Working out of the random signals models. Komponents Technol. 11, 146-151 (2007) (In Russian) [2] Machehin, Yu.: Estimation of result of measurements of instability of frequency outcomes of lasers, on a basis fractal properties diffusion processes. Sistemi obrobki informatsii 4(71), 139-142 (2008) (In Russian) [3] Kahane, J.-P.: Some random series of functions. In: Cambridge Studies in Advanced Mathematics, vol. 5. Cambridge University Press, Cambridge (1985) · Zbl 0571.60002 [4] Doobko, V.A., Karachanskaya, E.V.: Classification and simulation of the Random Harmonic Processes on the base of SHCS - series. Yakutian Math. J. 18, 36-54 (2011) (In Russian) · Zbl 1274.60115 [5] Cook, Ch.E., Bernfield, M.: Radar Signals. An Introduction to Theory and Application. Advanced Radar Studies Department Sperry Gyroscope Company, Great Neck, Long Island, New York (1967) [6] Kolachevskiy, N.N.: Magnetic Noise. Nauka, Moscow (1971) (in Russian) [7] Yaglom, A.M.: An Introduction to the Theory of Stationary Random Functions. Dover Publications Inc., Mineola, NY (2004) [8] Yaglom, A.M.: Correlation Theory of Stationary and Related Random Functions. Vol. 1: Basic Results. Springer, New York (1987) · Zbl 0685.62078 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.