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.