Abstract
Here we analyze different ways of describing hyper-random variables and processes with respect to appropriateness of their use in different types of transforms. We present relationships between the characteristics and parameters of the original and transformed hyper-random variables and processes, and then develop recommendations for the use of the various ways of describing hyper-random variables in the case of linear and nonlinear transforms, and hyper-random processes in the case of both inertialess and inertial transforms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Gorban, I.I.: Teoriya Ymovirnostey i Matematychna Statystika dlya Naukovykh Pratsivnykiv ta Inzheneriv (Probability Theory and Mathematical Statistics for Scientists and Engineers). IMMSP, NAS of Ukraine, Kiev (2003)
Gorban, I.I.: Transformation of hyper-random quantities and processes. Radioelectronics and Communications System 53(2), 59–73 (2010)
Gorban, I.I.: Teoriya Gipersluchainykh Yavleniy: Phyzicheskie i Matematicheskie Osnovy (The Theory of Hyper-random Phenomena: Physical and Mathematical Basis). Naukova dumka, Kiev (2011)
Gorban, I.I.: Fenomen Statisticheskoy Ustoichivosti (The Phenomenon of Statistical Stability). Naukova dumka, Kiev (2014)
Levin, B.R.: Teoreticheskie Osnovy Statisticheskoy Radiotekhniki (Theoretical Basis of Statistical Radio Engineering), 1, Sovetskoe Radio, Moscow (1974)
Tikhonov, V.I., Kharisov, V.N.: Statisticheskiy Analiz i Sintez Radiotekhnicheskikh Ustroystv i System (Statistical Analysis and Synthesis of Wireless Devices and Systems). Radio i svyaz, Moscow (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Gorban, I.I. (2017). Transformations of Hyper-random Variables and Processes. In: The Statistical Stability Phenomenon. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-43585-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-43585-5_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43584-8
Online ISBN: 978-3-319-43585-5
eBook Packages: EngineeringEngineering (R0)