Kolmogorov's law of the iterated logarithm for noncommutative martingales

TL;DR

This paper establishes a noncommutative version of Kolmogorov's law of the iterated logarithm for martingales, extending classical probability results into the noncommutative setting with new exponential inequalities.

Contribution

It introduces a noncommutative analogue of Kolmogorov's law of the iterated logarithm for martingales, building on recent exponential inequalities.

Findings

Proves Kolmogorov's law for noncommutative martingales.

Extends classical probability results to noncommutative frameworks.

Utilizes recent exponential inequalities by Junge and the author.

Abstract

We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved recently by Junge and the author.