On Bernstein Type Exponential Inequalities for Matrix Martingales
Probability
2021-03-26 v1
Abstract
In this work, Bernstein's concentration inequalities for squared integrable matrix-valued discrete-time martingales are obtained. Based on Lieb's theory and Bernstein's condition, a suitable supermartingale can be constructed. Our proof is largely based on this new exponential supermartingale, Freedman's method, and Doob's stopping theorem. Our result can be regarded as an extension of Tropp's work (ECP, 2012).
Keywords
Cite
@article{arxiv.2103.13690,
title = {On Bernstein Type Exponential Inequalities for Matrix Martingales},
author = {Zijie Tian},
journal= {arXiv preprint arXiv:2103.13690},
year = {2021}
}
Comments
11 pages. All comments are welcome