In this paper, 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 %, with a given constant, gradient. We also present various examples of spaces possessing the latter property.
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Preprint, ISyE, Georgia Institute of Technology, 765 Ferst Dr. NW Atlanta GA 30332-0205
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View Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces