Abstract
Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions. and mean metric of order q.
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Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01920).
Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow. Russia. 1996. Part II.
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Szeidl, L., Zolotarev, V.M. The central limit theorem without the condition of independence. J Math Sci 91, 3002–3004 (1998). https://doi.org/10.1007/BF02432872
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DOI: https://doi.org/10.1007/BF02432872