  The moment sum of squares (moment-SOS) hierarchy produces sequences of upper
and lower bounds on functionals of the exit time solution of a polynomial
stochastic differential equation with polynomial constraints, at the price of
solving semidefinite optimization problems of increasing size. In this note we
use standard results from elliptic partial differential equation analysis to
prove convergence of the bounds produced by the hierarchy. We also use
elementary convex analysis to describe a super- and sub-solution interpretation
dual to a linear formulation on occupation measures. The practical relevance of
the hierarchy is illustrated with numerical examples.
