RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2011 Volume 396, Pages 93–101 (Mi znsl4653)

This article is cited in 3 papers

Optimal estimates for the rate of strong Gaussian approximation in the infinite dimensional invariance principle

A. Yu. Zaitsevab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia

Abstract: Estimates for the rate of strong Gaussian approximation in the invariance principle in the Hilbert space for sums of i.i.d. random vectors are derived. It is shown that they are optimal with respect to the order if the sequence of eigenvalues of the covariance operator of summands decreases slowly.

Key words and phrases: invariance principle, strong approximation, convergence rates, Hilbert space, sums of independent random vectors.

UDC: 519.2

Received: 25.11.2011


 English version:
Journal of Mathematical Sciences (New York), 2013, 188:6, 689–693

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025