It is described how both plurisubharmonicity and convexity of functions can be characterized in terms of simple to work with classes of holomorphic martingales, namely a class of driftless Itô processes satisfying a skew-symmetry property and a family of linear modifications of Brownian motion parametrized by a compact set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-12,
author = {Maciej Klimek},
title = {Stochastic characterization of plurisubharmonicity and convexity of functions},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {175-181},
zbl = {1336.32031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-12}
}
Maciej Klimek. Stochastic characterization of plurisubharmonicity and convexity of functions. Banach Center Publications, Tome 104 (2015) pp. 175-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-12/