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Large Deviations of Vector-valued Martin...
Juditsky, Anatoli...
Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces by Juditsky, Anatoli ( Author )
N.A
04-09-2008
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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http://arxiv.org/abs/0809.0813
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