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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1978 Volume 23, Issue 3, Pages 684–688 (Mi tvp3093)

This article is cited in 11 papers

Short Communications

Some improvements of convergence rate estimates in the central limit theorem

V. V. Ul'yanov

Moscow

Abstract: Four theorems on the rate of convergence in the central limit theorem are formulated in the paper. Theorems 1 and 2 deal with estimates in the case of independent not necessarily identically distributed real random variables (r. v.), theorem 3 – in the case of independent identically distributed (i. i. d.) $R^k$-valued r. v., theorem 4 – in the case of i. i. d. Hilbert space valued r. v. These theorems improve some known results in [2]–[8]. The proofs will be published elsewhere.

Received: 10.04.1978


 English version:
Theory of Probability and its Applications, 1978, 23:3, 660–663

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