  The radiation (reaction, Robin) boundary condition for the continuum
diffusion equation is widely used in chemical and biological applications to
express reactive boundaries. The underlying trajectories of the diffusing
particles are believed to be partially absorbed and partially reflected at the
reactive boundary, however, the relation between the reaction (radiation)
constant in the Robin boundary condition and the reflection probability is
still unclear. In this paper we clarify the issue by finding the relation
between the reaction (radiation) constant and the absorption probability of the
diffusing trajectories at the boundary. We analyze the Euler scheme for the
underlying It\^o dynamics, which is assumed to have variable drift and
diffusion tensor, with partial reflection at the boundary. Trajectories that
cross the boundary are terminated with a given probability and otherwise are
reflected in a normal or oblique direction. We use boundary layer analysis of
the corresponding Wiener path integral to resolve the non-uniform convergence
of the probability density function of the numerical scheme to the solution of
the Fokker-Planck equation with the Robin boundary condition, as the time step
is decreased. We show that the Robin boundary condition is recovered in the
limit iff trajectories are reflected in the co-normal direction. We find the
relation of the reactive constant to the termination probability. We show the
effect of using the new relation in numerical simulations.
