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2016 Characterization of max-continuous local martingales vanishing at infinity
Beatrice Acciaio, Irina Penner
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP3963


We provide a characterization of the family of non-negative local martingales that have continuous running supremum and vanish at infinity. This is done by describing the class of random times that identify the times of maximum of such processes. In this way we extend to the case of general filtrations a result proved by Nikeghbali and Yor [21] for continuous filtrations. Our generalization is complementary to the one presented by Kardaras [15], and is obtained by means of similar tools.


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Beatrice Acciaio. Irina Penner. "Characterization of max-continuous local martingales vanishing at infinity." Electron. Commun. Probab. 21 1 - 10, 2016.


Received: 3 December 2014; Accepted: 27 September 2016; Published: 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1354.60045
MathSciNet: MR3564218
Digital Object Identifier: 10.1214/16-ECP3963

Primary: 60G07 , 60G44

Keywords: honest time , local martingale , predictable set , predictable stopping time , time of maximum

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