  In this short article we present new results that bring about hitherto
unknown relations between certain Bernstein diffusions wandering in bounded
convex domains of Euclidean space on the one hand, and processes which
typically occur in forward-backward systems of stochastic differential
equations on the other hand. A key point in establishing such relations lies in
the fact that the Bernstein diffusions we consider are actually reversible
It\^o diffusions.
