## Differential and Integral Equations

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

#### Abstract

We give a self-contained and short proof for the existence, uniqueness and measurability of the $p$-harmonious functions in the case $2\le p < \infty$. 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.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 201-216.

Dates
First available in Project Euclid: 30 January 2014

Luiro, Hannes; Parviainen, Mikko; Saksman, Eero. On the existence and uniqueness of $p$-harmonious functions. Differential Integral Equations 27 (2014), no. 3/4, 201--216. https://projecteuclid.org/euclid.die/1391091363