Comptes Rendus
no. 2
Probability Theory
Representation theorems for generators of backward stochastic differential equations
Paul Malliavin
Long Jiang1, 2
1Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
2School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
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

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

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

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

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

Cited by Sources:

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

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