Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Kolmogorov’s law of the iterated logarithm for noncommutative martingales

Qiang Zeng

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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.

Résumé

Nous prouvons la loi de Kolmogorov du logarithme itéré pour des martingales non-commutatives. Le cas commutatif a été établi par Stout. L’ingrédient clé est une inégalité exponentielle prouvée récemment par Junge et l’auteur.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 1124-1130.

Dates
Received: 5 August 2013
Revised: 12 January 2014
Accepted: 22 January 2014
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1435759242

Digital Object Identifier
doi:10.1214/14-AIHP603

Mathematical Reviews number (MathSciNet)
MR3365975

Zentralblatt MATH identifier
1335.46058

Subjects
Primary: 46L53: Noncommutative probability and statistics 60F15: Strong theorems

Keywords
Law of the iterated logarithm Noncommutative martingales Quantum martingales Exponential inequality

Citation

Zeng, Qiang. Kolmogorov’s law of the iterated logarithm for noncommutative martingales. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 1124--1130. doi:10.1214/14-AIHP603. https://projecteuclid.org/euclid.aihp/1435759242


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