Open Access
November 2020 Convergence of local supermartingales
Martin Larsson, Johannes Ruf
Ann. Inst. H. Poincaré Probab. Statist. 56(4): 2774-2791 (November 2020). DOI: 10.1214/20-AIHP1058


We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of stationarily local integrability plays a key role.

Nous caractérisons l’événement de convergence d’une surmartingale locale. Les conditions sont exprimées en termes de ses caractéristiques prévisibles et de sa variation quadratique. La notion d’intégrabilité stationnairement locale joue un rôle clé.


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Martin Larsson. Johannes Ruf. "Convergence of local supermartingales." Ann. Inst. H. Poincaré Probab. Statist. 56 (4) 2774 - 2791, November 2020.


Received: 20 August 2018; Revised: 10 February 2020; Accepted: 11 March 2020; Published: November 2020
First available in Project Euclid: 21 October 2020

MathSciNet: MR4164856
Digital Object Identifier: 10.1214/20-AIHP1058

Primary: 60G07
Secondary: 60G17 , 60G44

Keywords: Stationary localization , Supermartingale convergence

Rights: Copyright © 2020 Institut Henri Poincaré

Vol.56 • No. 4 • November 2020
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