  In this article, we consider non-smooth time-dependent domains and
single-valued, smoothly varying directions of reflection at the boundary. In
this setting, we first prove existence and uniqueness of strong solutions to
stochastic differential equations with oblique reflection. Secondly, we prove,
using the theory of viscosity solutions, a comparison principle for fully
nonlinear second-order parabolic partial differential equations with oblique
derivative boundary conditions. As a consequence, we obtain uniqueness, and, by
barrier construction and Perron's method, we also conclude existence of
viscosity solutions. Our results generalize two articles by Dupuis and Ishii to
time-dependent domains.
