A Note on FBSDE characterization of mean exit times

Cloud Makasu

doi:10.1016/j.crma.2009.06.006

Probability Theory

A Note on FBSDE characterization of mean exit times
[Caractérisation des temps de sortie moyens pour une équation FBSDE]

Présenté par : Paul Deheuvels

Cloud Makasu ¹

¹ Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 965-969.

Résumé
Abstract

Dans cette Note on donne une nouvelle caractérisation explicite des temps de sortie moyens pour un probléme récemment introduit par l'auteur ; cette caractérisation est obtenue à partir d'une FBSDE quadratique à temps terminal aléatoire. On démontre aussi, sous certaines conditions, une estimation a priori, et un résultat d'unicité pour ce type d'équation différentielle stochastique directe et rétrograde.

In this Note, we present a new explicit characterization for a mean exit time problem recently treated by the author, in form of a quadratic Forward–Backward Stochastic Differential Equation (FBSDE) with a random terminal time. An a priori estimate and a uniqueness result for such a type of FBSDE are also proved, under certain conditions.

Reçu le : 2009-03-03
Accepté le : 2009-04-15
Publié le : 2009-06-30

DOI : 10.1016/j.crma.2009.06.006

Affiliations des auteurs :

Cloud Makasu ¹

¹ Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

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     title = {A {Note} on {FBSDE} characterization of mean exit times},
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Cloud Makasu. A Note on FBSDE characterization of mean exit times. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 965-969. doi : 10.1016/j.crma.2009.06.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.006/

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Cité par Sources :

^☆ Partial results of this Note were obtained when the author was holding a postdoc grant PRO12/1003 at the Mathematics Institute, University of Oslo, Norway.

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