Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls

A. A. Naumov^a^,^b^,*, V. G. Spokoiny^a^,^b^,^c^,^d, Yu. E. Tavyrikov^a, and V. V. Ulyanov^a^,^e
Translated by I. Ruzanova

^aNational Research University Higher School of Economics, Moscow, Russia

^bInstitute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

^cWeierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

^dHumboldt University of Berlin, Berlin, Germany

^eFaculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

Correspondence to: *e-mail: anaumov@hse.ru

Received 7 May, 2018

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.

DOI: 10.1134/S1064562418060248