On the existence and uniqueness of p-harmonious functions

preprint2012arXivOpen access

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.

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On the existence and uniqueness of p-harmonious functions

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