A matrix Burkholder-Davis-Gundy inequality
Probability
2026-03-03 v2
Abstract
We prove an inequality for the spectral norm of matrix valued stochastic integrals. This inequality can be seen either as a non-commutative version of the Burkholder-Davis-Gundy inequality or as an extension of the non-commutative Khintchine inequality of Lust-Piquard to stochastic integrals. The proof relies on a version of Freedman's inequality for matrix valued martingales.
Keywords
Cite
@article{arxiv.2505.07389,
title = {A matrix Burkholder-Davis-Gundy inequality},
author = {Tom Maître},
journal= {arXiv preprint arXiv:2505.07389},
year = {2026}
}