Forward-Backward Stochastic Differential Equations Generated by Bernstein Diffusions
نویسنده
چکیده
In this Note we present new results which bring about hitherto unknown relations between certain Bernstein di¤usions wandering in bounded convex domains of Euclidean space on the one hand, and processes which typically occur in forward-backward systems of stochastic di¤erential equations on the other hand. A key point in establishing such relations is the fact that the Bernstein di¤usions we consider are actually reversible Itô di¤usions. Résumé. Dans cette Note nous présentons des résultats nouveaux mettant en évidence certaines relations jusquici inconnues entre certaines di¤usions de Bernstein évoluant dans des domaines convexes bornés de lespace euclidien dune part, et des processus apparaissant typiquement dans des systèmes progressifs-rétrogrades déquations di¤érentielles stochastiques dautre part. Un point clé permettant détablir de telles relations est que les di¤usions de Bernstein que nous considérons sont en fait des di¤usions dItô réversibles.
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