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Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls

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Abstract

Upper bounds for the closeness of two centered Gaussian measures in the class of balls in a separable Hilbert space are obtained. The bounds are optimal with respect to the dependence on the spectra of the covariance operators of the Gaussian measures. The inequalities cannot be improved in the general case.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    A. A. Naumov, V. G. Spokoiny, Yu. E. Tavyrikov & V. V. Ulyanov

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    A. A. Naumov & V. G. Spokoiny

  3. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    V. G. Spokoiny

  4. Humboldt University of Berlin, Berlin, Germany

    V. G. Spokoiny

  5. Moscow State University, Moscow, Russia

    V. V. Ulyanov

Authors
  1. A. A. Naumov
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  2. V. G. Spokoiny
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  3. Yu. E. Tavyrikov
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  4. V. V. Ulyanov
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Corresponding author

Correspondence to A. A. Naumov.

Additional information

Original Russian Text © A.A. Naumov, V.G. Spokoiny, Yu.E. Tavyrikov, V.V. Ulyanov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 5.

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Naumov, A.A., Spokoiny, V.G., Tavyrikov, Y.E. et al. Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls. Dokl. Math. 98, 490–493 (2018). https://doi.org/10.1134/S1064562418060248

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  • DOI: https://doi.org/10.1134/S1064562418060248

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