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Probabilities of moderate deviations in a Banach space. (English) Zbl 0475.60005


MSC:

60B11 Probability theory on linear topological spaces
60F10 Large deviations
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[1] R. R. Bahadur and S. L. Zabell, Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979), no. 4, 587 – 621. · Zbl 0424.60028
[2] A. A. Borovkov and A. A. Mogul\(^{\prime}\)skiĭ, Probabilities of large deviations in topological spaces. I, Sibirsk. Mat. Zh. 19 (1978), no. 5, 988 – 1004, 1213 (Russian). · Zbl 0397.60029
[3] H. Cramér, Sur un nouveau théorème limite de la probabilité, Actualités Sci. Indust. 736 (1938), 5-23. · JFM 64.0529.01
[4] William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. · Zbl 0077.12201
[5] Tze Leung Lai, Limit theorems for delayed sums, Ann. Probability 2 (1974), 432 – 440. · Zbl 0305.60009
[6] Tze Leung Lai, On \?-quick convergence and a conjecture of Strassen, Ann. Probability 4 (1976), no. 4, 612 – 627. · Zbl 0369.60036
[7] Herman Rubin and J. Sethuraman, Probabilities of moderatie deviations, Sankhyā Ser. A 27 (1965), 325 – 346.
[8] A. D. Slastnikov, Limit theorems for probabilities of moderate deviations, Teor. Verojatnost. i Primenen. 23 (1978), no. 2, 340 – 357 (Russian, with English summary). · Zbl 0405.60032
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