Uniqueness result for the BSDE whose generator is monotonic in <i>y</i> and uniformly continuous in <i>z</i>

Sheng-Jun Fan; Long Jiang

doi:10.1016/j.crma.2009.10.023

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

Sheng-Jun Fan ¹ ; Long Jiang ¹

¹ College of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221116, PR China

Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 89-92.

Résumé
Abstract

Dans cette Note on démontre que si g est continue, monotone, de croissance quelconque en y, g uniformément continue en z et $(g {(t, 0, 0))}_{t \in [0, T]}$ 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 $(g {(t, 0, 0))}_{t \in [0, T]}$ 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 : 2009-01-24
Accepté le : 2009-10-06
Publié le : 2009-12-22

DOI : 10.1016/j.crma.2009.10.023

Affiliations des auteurs :

Sheng-Jun Fan ¹ ; Long Jiang ¹

¹ College of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221116, PR China

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     author = {Sheng-Jun Fan and Long Jiang},
     title = {Uniqueness result for the {BSDE} whose generator is monotonic in \protect\emph{y} and uniformly continuous in \protect\emph{z}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {89--92},
     publisher = {Elsevier},
     volume = {348},
     number = {1-2},
     year = {2010},
     doi = {10.1016/j.crma.2009.10.023},
     language = {en},
}

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Sheng-Jun Fan; Long Jiang. Uniqueness result for the BSDE whose generator is monotonic in y and uniformly continuous in z. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 89-92. doi : 10.1016/j.crma.2009.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.023/

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Cité par Sources :

^☆ 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.

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