Approximation of convolutions of multidimensional distributions

One obtains estimates for the accuracy of the approximation of the distributions of sums of independent random vectors, concentrated in a ball of radius within the accuracy of a small probability P, with the aid of various approximating distributions in the Lévy-Prokhorov metric.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 68–80, 1985.