Abstract:
The problem under consideration is to estimate the distance, with respect to a chosen metric μμ, between two linear combinations X=∑jcjXjX=∑jcjXj and Y=∑jcjYjY=∑jcjYj of independent random variables with values in a Banach space UU.
General results of this paper enable, in particular, to effectively estimate the accuracy of approximation of the distributions of normalized sums of independent random UU-valued variables by a normal law.
When choosing μμ in an appropriate way, one obtains estimates quite analogous to those known in the simplest case U=R1U=R1.
Citation:
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