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Martingale convergence to infinitely divisible laws with finite variances. (English) Zbl 0228.60011


MSC:

60F05 Central limit and other weak theorems
60E07 Infinitely divisible distributions; stable distributions
60G42 Martingales with discrete parameter
60G44 Martingales with continuous parameter
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References:

[1] G. M. Bavli, Über einige Verallgemeinerungen der Grenzwertsätze der Wahrscheinlichkeitsrechnung, Mat. Sb. 1 (43) (1936), 917-930. · JFM 62.0593.01
[2] Patrick Billingsley, The Lindeberg-Lévy theorem for martingales, Proc. Amer. Math. Soc. 12 (1961), 788 – 792. · Zbl 0129.10701
[3] B. M. Brown, Martingale central limit theorems, Ann. Math. Statist. 42 (1971), 59 – 66. · Zbl 0218.60048 · doi:10.1214/aoms/1177693494
[4] B. V. Gnedenko, Kurs teorii veroyatnosteĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit.,], Moscow-Leningrad, 1950 (Russian). · Zbl 0041.24702
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