Comptes Rendus
no. 8
Harmonic analysis/Probability theory
Distribution of martingales with bounded square functions

Presented by: the Editorial Board

Dmitriy M. Stolyarov1, 2; Vasily Vasyunin1, 2; Pavel Zatitskiy1, 2; Ilya Zlotnikov1, 3
1 St. Petersburg State University, Department of Mathematics and Computer Science, 14th line 29B, Vailuevsky Island, St. Petersburg, Russia
2 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia
3 Department of Mathematics and Physics, University of Stavanger, Stavanger, Norway
Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 671-675.

We study the terminate distribution of a martingale whose square function is bounded. We obtain sharp estimates for the exponential and p-moments, as well as for the distribution function itself. The proofs are based on the elaboration of the Burkholder method and on the investigation of certain locally concave functions.

Nous étudions la distribution terminée d'une martingale dont la fonction carrée est bornée. Nous obtenons les estimations les meilleures possibles pour les p-moments et les moments exponentiels. Un développement de la méthode de Burkholder et les études sur des fonctions localement infléchies servent de base aux démonstrations.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.08.003

Dmitriy M. Stolyarov 1, 2; Vasily Vasyunin 1, 2; Pavel Zatitskiy 1, 2; Ilya Zlotnikov 1, 3

1 St. Petersburg State University, Department of Mathematics and Computer Science, 14th line 29B, Vailuevsky Island, St. Petersburg, Russia
2 St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia
3 Department of Mathematics and Physics, University of Stavanger, Stavanger, Norway 
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Dmitriy M. Stolyarov; Vasily Vasyunin; Pavel Zatitskiy; Ilya Zlotnikov. Distribution of martingales with bounded square functions. Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 671-675. doi : 10.1016/j.crma.2019.08.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.08.003/

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