A Probabilistic Characterization of g-Harmonic Functions

A Probabilistic Characterization of g-Harmonic Functions

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Associated with a quasi-linear generator function g, we give a definition of g-harmonic functions.The relation Dryer Parts between the g-harmonic functions and g-martingales will be delineated.It is direct to construct such relation for smooth case, but for continuous case we need the theory of viscosity solution.

Under Hardware the nonlinear expectation mechanism, we can also get the similar relation between harmonic functions and martingales.The strict converse problem of mean value property of g-harmonic functions are discussed finally.