The aim of this note is to revisit the connections between some stochastic games, namely
Tug-of-War games, and a class of nonlocal PDEs on graphs. We consider a general …

In this article, we study the ω-diffusion equation on a graph with Dirichlet boundary
conditions ut (x, t)=∆ ωu (x, t)+ eβtup (x, t),(x, t)∈ S×(0,∞), u (x, t)= 0,(x, t)∈∂ S×[0,∞), u (x …

In this article, we study the two membranes problem for operators given in terms of a mean
value formula on a regular tree. We show existence of solutions under adequate conditions …

In this paper, we study the Dirichlet problem for systems of mean value equations on a
regular tree. We deal both with the directed case (the equations verified by the components …

We introduce two notions of convexity for an infinite regular tree. For these two notions we
show that given a continuous boundary datum there exists a unique convex envelope on the …

In this paper we study the Dirichlet-to-Neumann map for solutions to mean value formulas
on trees. We give two alternative definition of the Dirichlet-to-Neumann map. For the first …