Probability Theory
Representation theorems for generators of backward stochastic differential equations
Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 161-166.

It is proved that the generator g of a backward stochastic differential equation (BSDE) can be represented by the solutions of the corresponding BSDEs if and only if g is a Lebesgue generator.

Dans cette Note on montre que le générateur g d'une équation stochastique rétrograde (EDSR) peut être représentré par la solution de l'EDSR correspondante si et seulement si g est un générateur de Lebesgue.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.10.023
Jiang, Long 1, 2

1 Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
2 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
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Jiang, Long. Representation theorems for generators of backward stochastic differential equations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 161-166. doi : 10.1016/j.crma.2004.10.023. http://www.numdam.org/articles/10.1016/j.crma.2004.10.023/

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[2] Chen, Z. A property of backward stochastic differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 326 (1998) no. 4, pp. 483-488

[3] Coquet, F.; Hu, Y.; Mémin, J.; Peng, S. A general converse comparison theorem for backward stochastic differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 333 (2001), pp. 577-581

[4] Hewitt, E.; Stromberg, K.R. Real and Abstract Analysis, Springer-Verlag, New York, 1978

[5] Jiang, L. Some results on the uniqueness of generators of backward stochastic differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004) no. 7, pp. 575-580

[6] Pardoux, E.; Peng, S. Adapted solution of a backward stochastic differential equation, Systems Control Lett., Volume 14 (1990), pp. 55-61

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Supported by the National Natural Science Foundation of China (No. 10131030) and Science Foundation of CUMT.