Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Probabilities of moderate deviations in a Banach space


Authors: Chandrakant M. Deo and Gutti Jogesh Babu
Journal: Proc. Amer. Math. Soc. 83 (1981), 392-397
MSC: Primary 60F10; Secondary 60B12
DOI: https://doi.org/10.1090/S0002-9939-1981-0624938-3
MathSciNet review: 624938
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. R. Bahadur and S. L. Zabell, Large deviations of the sample mean in general vector spaces, Ann. Probab. 7 (1979), 587-621. MR 537209 (80i:60031)
  • [2] A. A. Borovkov and A. A. Mogul'skii, Probabilities of large deviations in topological spaces. I, Siberian Math. J. 19 (1978), 697-709. MR 508496 (80c:60045)
  • [3] H. Cramér, Sur un nouveau théorème limite de la probabilité, Actualités Sci. Indust. 736 (1938), 5-23.
  • [4] W. Feller, An introduction to probability theory and its applications, vol. II, 2nd ed., Wiley, New York, 1971. MR 0270403 (42:5292)
  • [5] T. L. Lai, Limit theorems for delayed sums, Ann. Probab. 2 (1974), 432-441. MR 0356193 (50:8664)
  • [6] -, On $ r$-quick convergence and a conjecture of Strassen, Ann. Probab. 4 (1976), 612-627. MR 0431326 (55:4327)
  • [7] H. Rubin and J. Sethuraman, Probabilities of moderate deviations, Sankhyā Ser. A 27 (1965), 325-346. MR 0203783 (34:3631)
  • [8] A. D. Slastnikov, Limit theorems for moderate deviation probabilities, Theory Probab. Appl. 23 (1978), 322-340. MR 0488238 (58:7799)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60F10, 60B12

Retrieve articles in all journals with MSC: 60F10, 60B12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624938-3
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society