An Introduction to the Theory of Stationary Random Functions

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Courier Corporation, 2004 - Mathematics - 235 pages
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This two-part treatment covers the general theory of stationary random functions and the Wiener-Kolmogorov theory of extrapolation and interpolation of random sequences and processes. Beginning with the simplest concepts, it covers the correlation function, the ergodic theorem, homogenous random fields, and general rational spectral densities, among other topics. Numerous examples appear throughout the text, with emphasis on the physical meaning of mathematical concepts. Although rigorous in its treatment, this is essentially an introduction, and the sole prerequisites are a rudimentary knowledge of probability and complex variable theory. 1962 edition.
 

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Contents

THE GENERAL THEORY OF STATIONARY
7
Definition of a Random Func
16
Differentiation and Integration of a Random Process
22
Examples
51
Examples of Correlation
61
FURTHER DEVELOPMENT OF THE CORRELATION THEORY OF RANDOM FUNCTIONS Page 78
78
LINEAR EXTRAPOLATION AND FILTERING
95
LINEAR FILTERING OF STATIONARY RANDOM
126
The Case of a General Rational Spectral
141
Statement of
150
The Case of a General
161
LINEAR FILTERING OF STATIONARY RANDOM
167
FURTHER DEVELOPMENT OF THE THEORY
182
GENERALIZED RANDOM PROCESSES Page
207
SOME RECENT DEVELOPMENTS Page
214
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About the author (2004)

Yaglom, Institute of Atmospheric Physics, Academy of Sciences, USSR.

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