Transactions of the American Mathematical Society

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

Author(s): Yijun Hu; Tzong-Yow Lee
Journal: Trans. Amer. Math. Soc. 355 (2003), 3047-3064.
MSC (2000): Primary 60F10
Posted: September 21, 2001
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60F10

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

DOI: 10.1090/S0002-9947-01-02893-8
PII: S 0002-9947(01)02893-8
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
Posted: September 21, 2001
Additional Notes: Supported in part by the National Natural Science Foundation of China and the Education Department of China.
Copyright of article: Copyright 2001, American Mathematical Society

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