Moderate deviation principles for trajectories of sums of independent Banach space valued random variables |
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Authors: | Yijun Hu Tzong-Yow Lee |
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Affiliation: | Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, People's Republic of China ; Department of Mathematics, University of Maryland, College Park, Maryland 20742 |
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Abstract: | Let be a sequence of i.i.d. random vectors with values in a separable Banach space. Moderate deviation principles for trajectories of sums of 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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Keywords: | Moderate deviations trajectories functional law of the iterated logarithm |
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