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# On the theory of random functions and the control of processes on the basis of incomplete data by Albert Nikolaevich Shiriaev

Written in English

## Subjects:

• Sequential analysis.

Edition Notes

Bibliography: p. 37-38.

## Book details

The Physical Object ID Numbers Statement by A.N. Shiryaev, Translated by A.S. Kosak and I. Selin. Series Memorandum -- RM-4527-PR, Research memorandum (Rand Corporation) -- RM-4527-PR.. Pagination v, 38 p. : Number of Pages 38 Open Library OL16647981M

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Kozak, Ivan Selin CitationAuthor: Albert Nikolaevich Shiriaev, Andrew S. Kozak, Ivan Selin. Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling-based method to determine the evolution of uncertainty in a dynamical system when there is probabilistic uncertainty in the system parameters.

PC was first introduced by Norbert Wiener using Hermite polynomials to model stochastic processes with Gaussian random variables. It can be thought of as an extension of. Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems.

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In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random ically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such.

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Pugachev. This group includes the mean, standard deviation, range and distribution of data. SPC: This involves inspecting a random sample of the output from a process and deciding whether the characteristics of the products in the sample fall within a predetermined range. SPC is used to determine whether the process is functioning properly or not.

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Chapter 6 - Random Processes Recall that a random variable X is a mapping between the sample space S and the extended real line R+. That is, X: S R+. A random process (a.k.a stochastic process) is a mapping from the sample space into an ensemble of time functions (known as sample functions).

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