A Probabilistic Characterization of g-Harmonic Functions

Details A Probabilistic Characterization of g-Harmonic Functions A Probabilistic Characterization of g-Harmonic Functions

2011-08-12

arxiv.org/abs/1108.2558v3

Mathematics

Probability

Scientific paper

This paper gives a definition of g-harmonic functions and shows the relation between the g-harmonic functions and g-martingales. It's direct to construct such relation under smooth case, but for continuous case we need the theory of viscosity solution. The results show that under the nonlinear expectation mechanism, we also can get the similar relation between harmonic functions and martingales. Finally, we will give a result about the strict converse problem of mean value property of g-harmonic functions.

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