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On normal approximation in infinite-dimensional spaces. (English. Russian original) Zbl 0591.60032
Sov. Math., Dokl. 30, 548-553 (1984); translation from Dokl. Akad. Nauk SSSR 278, 1291-1296 (1984).
This paper deals with the central limit theorem in infinite-dimensional spaces and its estimate of convergence rate. There are six theorems in this paper. These theorems discuss the above problems with respect to Hilbert space, Banach space, \(\ell_{2p}\) space, U-statistics and \(L^ p(Y,\mu)\) respectively.
Many results are of ideal forms, they are comparable with the corresponding results in the case of i.i.d. r.v. Therefore the results of this paper are very important and widely interesting. But it ought to be pointed out that Chinese researchers have got finer and more exact results about U-statistics.
Reviewer: Su Chun
60F17 Functional limit theorems; invariance principles
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60F05 Central limit and other weak theorems