  This paper presents a finite-dimensional approximation for a class of partial
differential equations on the space of probability measures. These equations
are satisfied in the sense of viscosity solutions. The main result states the
convergence of the viscosity solutions of the finite-dimensional PDE to the
viscosity solutions of the PDE on Wasserstein space, provided that uniqueness
holds for the latter, and heavily relies on an adaptation of the Barles &
Souganidis monotone scheme to our context, as well as on a key precompactness
result for semimartingale measures. We illustrate this result with the example
of the Hamilton-Jacobi-Bellman and Bellman-Isaacs equations arising in
stochastic control and differential games, and propose an extension to the case
of path-dependent PDEs.
