Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces
Probability
2023-01-31 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.0809.0813,
title = {Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces},
author = {Anatoli Juditsky and Arkadii S. Nemirovski},
journal= {arXiv preprint arXiv:0809.0813},
year = {2023}
}