Forward-backward systems of stochastic differential equations generated by Bernstein diffusions

Ana Bela Cruzeiro, Pierre-A. Vuillermot

Published 2013-05-19Version 1

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.