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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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