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The Accuracy of Gaussian Approximation in Banach Spaces

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Limit Theorems of Probability Theory

Abstract

Let B be a real separable Banach space with norm || · || = || · || B . Suppose that X, X 1, X 2, … ∈ B are independent and identically distributed (i.i.d.) random elements (r.e.’s) taking values in B. Furthermore, assume that EX = 0 and that there exists a zero-mean Gaussian r.e. Y ∈ B such that the covariances of X and Y coincide.

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  1. V. Bentkus
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  2. F. Götze
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  1. Steklov Mathematical Institute, ul. Gubkina 8, 117966, Moscow, Russia

    Yu. V. Prokhorov

  2. Institute of Mathematics and Informatics, Lithuanian Academy of Sciences, Akademijos 4, 2600, Vilnius, Lithuania

    V. Statulevičius

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Bentkus, V., Götze, F., Paulauskas, V., Račkauskas, A. (2000). The Accuracy of Gaussian Approximation in Banach Spaces. In: Prokhorov, Y.V., Statulevičius, V. (eds) Limit Theorems of Probability Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04172-7_2

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  • DOI: https://doi.org/10.1007/978-3-662-04172-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08170-5

  • Online ISBN: 978-3-662-04172-7

  • eBook Packages: Springer Book Archive

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