On Bernstein Type Exponential Inequalities for Matrix Martingales

2021/03/25 by Tian, Zijie
#60E15 #60G42 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.13690

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).

Related

• Concentration for matrix martingales in continuous time and microscopic\n activity of social networks
• Bernstein-type and Bennett-type inequalities for unbounded matrix martingales
• Sharp Finite-Time Iterated-Logarithm Martingale Concentration
• On Bernstein Type Inequalities for Stochastic Integrals of Multivariate Point Processes
• Matrix Moment and Concentration Inequalities for Martingales and Ergodic Markov Chains with Applications in Statistical Learning