## Rates for the CLT via new ideal metrics.(English)Zbl 0675.60018

Let $$(B,\| \cdot \|)$$ be a separable Banach space, $$X=X(B)$$ the vector space of all random variables taking values in B. New ideal probability metrics of convolution type for the space X are introduced and it is shown that they provide refined rates of convergence of the sum $$S_ n=n^{-1/\alpha}(X_ 1+...+X_ n)$$ of i.i.d. random variables in X(B) to a stable limit law $$Y_{\alpha}$$ in X(B), where $$\alpha\in (0,2]$$.
Reviewer: N.Leonenko

### MSC:

 60F05 Central limit and other weak theorems 60G50 Sums of independent random variables; random walks 60E07 Infinitely divisible distributions; stable distributions 60B10 Convergence of probability measures 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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