Distribution of martingales with bounded square functions

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

doi:10.1016/j.crma.2019.08.003

Harmonic analysis/Probability theory

Distribution of martingales with bounded square functions
[La distribution des martingales dont les fonctions carrées sont bornées]

Présenté par : the Editorial Board

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

Comptes Rendus. Mathématique, Tome 357 (2019) no. 8, pp. 671-675.

Résumé
Abstract

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.

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.

Reçu le : 2018-10-10
Accepté le : 2019-08-05
Publié le : 2019-08-01

DOI : 10.1016/j.crma.2019.08.003

Affiliations des auteurs :

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

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     title = {Distribution of martingales with bounded square functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {671--675},
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Stolyarov, Dmitriy M.; Vasyunin, Vasily; Zatitskiy, Pavel; Zlotnikov, Ilya. Distribution of martingales with bounded square functions. Comptes Rendus. Mathématique, Tome 357 (2019) no. 8, pp. 671-675. doi : 10.1016/j.crma.2019.08.003. http://archive.numdam.org/articles/10.1016/j.crma.2019.08.003/

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