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Doklady Mathematics

, Volume 98, Issue 2, pp 490–493 | Cite as

Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls

  • A. A. Naumov
  • V. G. Spokoiny
  • Yu. E. Tavyrikov
  • V. V. Ulyanov
Mathematics
  • 2 Downloads

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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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. A. Naumov
    • 1
    • 2
  • V. G. Spokoiny
    • 1
    • 2
    • 3
    • 4
  • Yu. E. Tavyrikov
    • 1
  • V. V. Ulyanov
    • 1
    • 5
  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia
  3. 3.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  4. 4.Humboldt University of BerlinBerlinGermany
  5. 5.Moscow State UniversityMoscowRussia

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