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Averages

In: Probability, Random Processes, and Ergodic Properties

Author

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  • Robert M. Gray

    (Stanford University, Department of Electrical Engineering)

Abstract

The basic focus of classical ergodic theory was the development of conditions under which sample or time averages consisting of arithmetic means of a sequence of measurements on a random process converged to a probabilistic or ensemble average of the measurement as expressed by an integral of the measurement with respect to a probability measure. Theorems relating these two kinds of averages are called ergodic theorems.

Suggested Citation

  • Robert M. Gray, 1988. "Averages," Springer Books, in: Probability, Random Processes, and Ergodic Properties, chapter 4, pages 92-132, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2024-2_4
    DOI: 10.1007/978-1-4757-2024-2_4
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