Introduction to Random Processes

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

Informacionno-technologicheskij vestnik ◽

10.21499/2409-1650-2018-1-84-93 ◽

2018 ◽

Vol 15 (1) ◽

pp. 84-93

Author(s):

V. I. Volovach ◽

V. M. Artyushenko

Keyword(s):

Spectral Characteristics ◽

Random Processes ◽

Spectral Densities ◽

Differential Systems ◽

Non Gaussian ◽

Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

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Probability and Random Processes

10.1093/oso/9780198821939.003.0002 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Random Processes ◽

Distribution Functions ◽

Basic Logic ◽

Heavy Tailed Distributions ◽

Random Components ◽

Classical Distribution ◽

Heavy Tailed ◽

Basic Facts ◽

Stochastic Events ◽

Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

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