On the existence and uniqueness of $p$-harmonious functions

By Hannes Luiro, Mikko Parviainen, Eero Saksman. Differential and Integral Equations, 2012

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We give a self-contained and short proof for the existence, uniqueness and measurability of so called $p$-harmonious functions. The proofs only use elementary analytic tools. As a consequence, we obtain existence, uniqueness and measurability of value functions for the tug-of-war game with noise.

Subfields: Control and Systems Engineering, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/43a9b79934302001b6fb225dc181008bd988c1c1