Comptes Rendus
no. 6
Probability Theory
On the set of solutions of a BSDE with continuous coefficient
[Sur l'ensemble des solutions d'une équation différentielle stochastique rétrograde avec coefficient continu]

Présenté par : Paul Malliavin

Guangyan Jia1 ; Shige Peng1
1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 395-397.

Nous prouvons dans cette Note que, si le coefficient g=g(t,y,z) d'une EDSR est continu et linéairement croissant en (y,z), alors il existe soit une seule solution soit une infinité non dénombrable de solutions.

In this Note we prove that, if the coefficient g=g(t,y,z) of a one-dimensional BSDE is assumed to be continuous and of linear growth in (y,z), then there exists either one or uncountably many solutions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.01.022
Guangyan Jia 1 ; Shige Peng 1

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China 
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Guangyan Jia; Shige Peng. On the set of solutions of a BSDE with continuous coefficient. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 395-397. doi : 10.1016/j.crma.2007.01.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.022/

[1] Ph. Briand; B. Delyon; Y. Hu; E. Pardoux; L. Stoica Lp solutions of backward stochastic differential equations, Stochastic Process. Appl., Volume 108 (2003), pp. 109-129

[2] M. Kobylanski Backward stochastic differential equations and partial differential equation with quadratic growth, Ann. Probab., Volume 28 (2000), pp. 259-276

[3] J.P. Lepeltier; J.S. Martin Backward stochastic differential equations with continuous coefficients, Statist. Probab. Lett., Volume 34 (1997), pp. 425-430

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

Cité par Sources :

⁎ The authors thank the NSF of China for partial support under grant No. 10131040 and grant No. 10671111.

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