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.
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.
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@article{CRMATH_2009__347_15-16_965_0, author = {Makasu, Cloud}, title = {A {Note} on {FBSDE} characterization of mean exit times}, journal = {Comptes Rendus. Math\'ematique}, pages = {965--969}, publisher = {Elsevier}, volume = {347}, number = {15-16}, year = {2009}, doi = {10.1016/j.crma.2009.06.006}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.006/} }
TY - JOUR AU - Makasu, Cloud TI - A Note on FBSDE characterization of mean exit times JO - Comptes Rendus. Mathématique PY - 2009 SP - 965 EP - 969 VL - 347 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.06.006/ DO - 10.1016/j.crma.2009.06.006 LA - en ID - CRMATH_2009__347_15-16_965_0 ER -
Makasu, Cloud. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.06.006/
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☆ 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.