  In this work we prove an analogue, for partial differential equations on the
space of probability measures, of the classical vanishing viscosity result
known for equations on the Euclidean space. Our result allows in particular to
show that the value function arising in various problems of classical mechanics
and games can be obtained as the limiting case of second order PDEs. The method
of proof builds on stochastic analysis arguments and allows for instance to
prove a Freindlin-Wentzell large deviation theorem for McKean-Vlasov equations.
