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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Moderate deviation principles for trajectories of sums of independent Banach space valued random variables
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by Yijun Hu and Tzong-Yow Lee PDF
Trans. Amer. Math. Soc. 355 (2003), 3047-3064 Request permission

Abstract:

Let $\{X_n\}$ be a sequence of i.i.d. random vectors with values in a separable Banach space. Moderate deviation principles for trajectories of sums of $\{X_n\}$ are proved, which generalize related results of Borovkov and Mogulskii (1980) and Deshayes and Picard (1979). As an application, functional laws of the iterated logarithm are given. The paper also contains concluding remarks, with examples, on extending results for partial sums to corresponding ones for trajectory setting.
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Additional Information
  • Yijun Hu
  • Affiliation: Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, People’s Republic of China
  • Email: yijunhu@public.wh.hb.cn
  • Tzong-Yow Lee
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • Email: tyl@math.umd.edu
  • Received by editor(s): March 28, 2001
  • Received by editor(s) in revised form: May 3, 2001
  • Published electronically: September 21, 2001
  • Additional Notes: Supported in part by the National Natural Science Foundation of China and the Education Department of China.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3047-3064
  • MSC (2000): Primary 60F10
  • DOI: https://doi.org/10.1090/S0002-9947-01-02893-8
  • MathSciNet review: 1974674