no. 1-2
Probability Theory
Uniqueness result for the BSDE whose generator is monotonic in y and uniformly continuous in z
[Un résultat d'unicité pour une équation différentielle stochastique rétrograde dont le générateur g est monotone en y et uniformément continue en z]

Présenté par : Paul Malliavin

Fan, Sheng-Jun1 ; Jiang, Long1
1 College of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221116, PR China
Comptes Rendus. Mathématique, Tome 348 (2010) no. 1-2, pp. 89-92.

Dans cette Note on démontre que si g est continue, monotone, de croissance quelconque en y, g uniformément continue en z et (g(t,0,0))t∈[0,T] est de carré intégrable, alors pour toute condition finale ξ de carré intégrable, en dimension un, l'équation différentielle stochastique rétrograde (BSDE) de générateur g, a une solution unique. Ce résultat généralise des résultats connus dans le cas de la dimension un.

In this Note, we prove that if g is continuous, monotonic and has a general growth in y, g is uniformly continuous in z, and (g(t,0,0))t∈[0,T] is square integrable, then for each square integrable terminal condition ξ, the one-dimensional backward stochastic differential equation (BSDE) with the generator g has a unique solution. This generalizes some corresponding (one-dimensional) results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.023
Fan, Sheng-Jun 1 ; Jiang, Long 1

1 College of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221116, PR China 
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Fan, Sheng-Jun; Jiang, Long. Uniqueness result for the BSDE whose generator is monotonic in y and uniformly continuous in z. Comptes Rendus. Mathématique, Tome 348 (2010) no. 1-2, pp. 89-92. doi : 10.1016/j.crma.2009.10.023. http://www.numdam.org/articles/10.1016/j.crma.2009.10.023/

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☆ Supported by the National Natural Science Foundation of China (No. 10671205), National Basic Research Program of China (No. 2007CB814901), Youth Foundation of China University of Mining & Technology (Nos. 2006A041 and 2007A029) and Qing Lan Project.