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arXiv · 1405.2639

Sharp Finite-Time Iterated-Logarithm Martingale Concentration

Akshay Balsubramani
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Abstract

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time version of the law of the iterated logarithm, and shed light on the relationship between it and the central limit theorem.

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BibTeXRIS

Akshay Balsubramani. 2014-05-12. Sharp Finite-Time Iterated-Logarithm Martingale Concentration. https://arxiv.org/abs/1405.2639

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