  Constrained diffusions in convex polyhedral domains with a general oblique
reflection field, and with a diffusion coefficient scaled by a small parameter,
are considered. Using an interior Dirichlet heat kernel lower bound estimate
for second order elliptic operators in bounded domains from [13], certain
uniform in the scaling parameter lower bounds on transition densities of such
constrained diffusions are established. These lower bounds together with
results from [1] give, under additional stability conditions, an exponential
leveling property, as the scaling parameter approaches zero, for exit times
from suitable bounded domains.
