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arXiv · 0809.0813

Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces

Anatoli Juditsky·Arkadii S. Nemirovski
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Abstract

We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so. We demonstrate that this is the case when the norm on the space can be approximated, within an absolute constant factor, by a norm which is differentiable on the unit sphere with a Lipschitz continuous gradient. We also present various examples of spaces possessing the latter property.

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Anatoli Juditsky, Arkadii S. Nemirovski. 2008-09-04. Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces. https://arxiv.org/abs/0809.0813

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