Forward-backward stochastic differential equations generated by Bernstein diffusions

Ana Bela Cruzeiro (1) , Pierre-A. Vuillermot (2)

1 ULISBOA - Universidade de Lisboa = University of Lisbon
2 IECL - Institut Élie Cartan de Lorraine

In this note we present new results which 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 is the fact that the Bernstein diffusions we consider are actually reversible Itô diffusions.

Mots clés: Parabolic equations; Bernstein diffusions

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Ana Bela Cruzeiro, Pierre-A. Vuillermot. Forward-backward stochastic differential equations generated by Bernstein diffusions. Stochastic Analysis and Applications, 2015, 33 (1), pp.91-109. ⟨10.1080/07362994.2014.968669⟩. ⟨hal-00819515⟩