Characterization of max-continuous local martingales vanishing at infinity
Probability
2016-10-03 v3
Abstract
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 [NY06] for continuous filtrations. Our generalization is complementary to the one presented by Kardaras [Kar14], and is obtained by means of similar tools.
Keywords
Cite
@article{arxiv.1412.1366,
title = {Characterization of max-continuous local martingales vanishing at infinity},
author = {Beatrice Acciaio and Irina Penner},
journal= {arXiv preprint arXiv:1412.1366},
year = {2016}
}