  In this paper, we study a two-point boundary value problem consisting of the
heat equation on the open interval $(0,1)$ with boundary conditions which
relate first and second spatial derivatives at the boundary points. Moreover,
the unique solution to this problem can be represented probabilistically in
terms of a sticky Brownian motion. This probabilistic representation is
attained from the stochastic differential equation for a sticky Brownian motion
on the bounded interval $[0,1]$.
