Lower bounds for the sharpness of a normal approximation in Banach spaces (Q1069548)

The author constructs an example of a random element in \(c_ 0\) (the space of sequences converging to zero) with zero mean with support in \(l_ 2\) where it is even bounded. It is shown that for the set of vectors with all coordinates smaller than r the central limit normal approximation with the corresponding Gaussian random vector has speed of convergence which is arbitrarily slow choosing the appropriate covariance kernel. This is essentially due to the missing smoothness of the boundary of the mentioned set.