Probabilities of moderate deviations in a Banach space

Deo, Chandrakant M.; Babu, Gutti Jogesh

doi:10.1090/S0002-9939-1981-0624938-3

Probabilities of moderate deviations in a Banach space
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by Chandrakant M. Deo and Gutti Jogesh Babu

Proc. Amer. Math. Soc. 83 (1981), 392-397

DOI: https://doi.org/10.1090/S0002-9939-1981-0624938-3

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Abstract:

We obtain probabilities of moderate deviations for i.i.d. sequences taking values in a separable Banach space under precise necessary and sufficient conditions. The results obtained are new even on the real line.

References

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. MR 537209
A. A. Borovkov and A. A. Mogul′skiĭ, Probabilities of large deviations in topological spaces. I, Sibirsk. Mat. Zh. 19 (1978), no. 5, 988–1004, 1213 (Russian). MR 508496

Sur un nouveau théorème limite de la probabilité

736

William Feller, An introduction to probability theory and its applications. Vol. II. , 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403
Tze Leung Lai, Limit theorems for delayed sums, Ann. Probability 2 (1974), 432–440. MR 356193, DOI 10.1214/aop/1176996658
Tze Leung Lai, On $r$-quick convergence and a conjecture of Strassen, Ann. Probability 4 (1976), no. 4, 612–627. MR 431326, DOI 10.1214/aop/1176996031
Herman Rubin and J. Sethuraman, Probabilities of moderatie deviations, Sankhyā Ser. A 27 (1965), 325–346. MR 203783
A. D. Slastnikov, Limit theorems for probabilities of moderate deviations, Teor. Verojatnost. i Primenen. 23 (1978), no. 2, 340–357 (Russian, with English summary). MR 0488238