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Stochastic characterization of plurisubharmonicity and convexity of functions. (English) Zbl 1336.32031

Białas-Cież, Leokadia (ed.) et al., Constructive approximation of functions. Selected papers based on the presentations at the conference, Bȩdlewo, Poland, June 29 – July 5, 2014. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-30-0/pbk). Banach Center Publications 107, 175-181 (2015).
Summary: 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.
For the entire collection see [Zbl 1337.41001].

MSC:

32U05 Plurisubharmonic functions and generalizations
32U15 General pluripotential theory
60J45 Probabilistic potential theory
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