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arXiv · 2505.07389

A matrix Burkholder-Davis-Gundy inequality

Tom Maître
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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.

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Tom Maître. 2025-05-12. A matrix Burkholder-Davis-Gundy inequality. https://arxiv.org/abs/2505.07389

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