Rates for the CLT via new ideal metrics (Q1122211)

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 \(\alpha\in (0,2]\).