On Linear Methods in Probability Theory

by K. Karhunen, Ivan Selin

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A summary of the most important properties of infinite sets of random variables, following Kolmogorov. The article constructs the Hilbert space corresponding to a given set of random variables with finite dispersions, discusses random functions and their simplest correlation properties, presents a new definition of the integral of a random function, defines the spectral representation of a random function, and considers applications of stationary random functions.

This report is part of the RAND Corporation Translation series. The translation was a product of the RAND Corporation from 1954 to 1961 that represented articles published in a foreign language and translated at RAND.

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