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arXiv · 2103.13690

On Bernstein Type Exponential Inequalities for Matrix Martingales

Zijie Tian
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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).

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Zijie Tian. 2021-03-25. On Bernstein Type Exponential Inequalities for Matrix Martingales. https://arxiv.org/abs/2103.13690

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