Abstract
The standard deviation, besides the expectation, is another important characteristic of a random variable. The covariance operator serves as a natural analogue of the standard deviation in the case of random elements. Covariance operators are symmetric positive operators which map spaces into their duals. We begin by studying general properties of such operators, and then turn to a study of covariance operators of random elements of weak order two. Throughout this chapter X, Y, Z (possibly with indices) stand for Banach spaces (unless explicitely stated otherwise).
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Vakhania, N.N., Tarieladze, V.I., Chobanyan, S.A. (1987). Covariance Operators. In: Probability Distributions on Banach Spaces. Mathematics and Its Application (Soviet Series), vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3873-1_3
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DOI: https://doi.org/10.1007/978-94-009-3873-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8222-8
Online ISBN: 978-94-009-3873-1
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