Representation theorems for generators of backward stochastic differential equations

Long Jiang

doi:10.1016/j.crma.2004.10.023

Probability Theory

Representation theorems for generators of backward stochastic differential equations
[Théorèmes de représentation pour générateurs d'équations différentielles stochastiques rétrogrades]

Présenté par : Paul Malliavin

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

Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 161-166.

Résumé
Abstract

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.

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.

Reçu le : 2004-06-17
Accepté le : 2004-09-19
Publié le : 2005-01-05

DOI : 10.1016/j.crma.2004.10.023

Affiliations des auteurs :

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

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     author = {Long Jiang},
     title = {Representation theorems for generators of backward stochastic differential equations},
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     number = {2},
     year = {2005},
     doi = {10.1016/j.crma.2004.10.023},
     language = {en},
}

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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.023/

Bibliographie
Cité par

[1] P. Briand; F. Coquet; Y. Hu; J. Mémin; S. Peng A converse comparison theorem for BSDEs and related properties of g-expectation, Electron. Commun. Probab., Volume 5 (2000), pp. 101-117

[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

Cité par Sources :

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

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