Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces
Juditsky, Anatoli ; Nemirovski, Arkadii S.
arXiv, 0809.0813 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2008-09-04
Classification:  Mathematics - Probability,  Mathematics - Statistics Theory 
@article{0809.0813,
     author = {Juditsky, Anatoli and Nemirovski, Arkadii S.},
     title = {Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0809.0813}
}

Juditsky, Anatoli; Nemirovski, Arkadii S. Large Deviations of Vector-valued Martingales in 2-Smooth Normed Spaces. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0809.0813/