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Moderate deviation principles for trajectories of sums of independent Banach space valued random variables


Authors: Yijun Hu and Tzong-Yow Lee
Journal: Trans. Amer. Math. Soc. 355 (2003), 3047-3064
MSC (2000): Primary 60F10
DOI: https://doi.org/10.1090/S0002-9947-01-02893-8
Published electronically: September 21, 2001
MathSciNet review: 1974674
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Abstract | References | Similar Articles | Additional Information

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

Keywords: Moderate deviations, trajectories, functional law of the iterated logarithm
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.
Article copyright: © Copyright 2001 American Mathematical Society