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

TL;DR

This paper uncovers new relationships between Bernstein diffusions, which are reversible Itô diffusions, and forward-backward stochastic differential equations within bounded convex domains, revealing previously unknown connections.

Contribution

It introduces novel links between Bernstein diffusions and forward-backward SDE systems, expanding understanding of their interplay in stochastic analysis.

Findings

Bernstein diffusions are reversible Itô diffusions.

Established relations between Bernstein diffusions and forward-backward SDEs.

New insights into stochastic processes in convex domains.

Abstract

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.