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

Jia, Guangyan1 ; Peng, Shige1
1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
Comptes Rendus. Mathématique, Tome 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
Jia, Guangyan 1 ; Peng, Shige 1

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China 
@article{CRMATH_2007__344_6_395_0,
     author = {Jia, Guangyan and Peng, Shige},
     title = {On the set of solutions of a {BSDE} with continuous coefficient},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {395--397},
     publisher = {Elsevier},
     volume = {344},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.01.022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.022/}
}
TY  - JOUR
AU  - Jia, Guangyan
AU  - Peng, Shige
TI  - On the set of solutions of a BSDE with continuous coefficient
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 395
EP  - 397
VL  - 344
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.01.022/
DO  - 10.1016/j.crma.2007.01.022
LA  - en
ID  - CRMATH_2007__344_6_395_0
ER  - 
%0 Journal Article
%A Jia, Guangyan
%A Peng, Shige
%T On the set of solutions of a BSDE with continuous coefficient
%J Comptes Rendus. Mathématique
%D 2007
%P 395-397
%V 344
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.01.022/
%R 10.1016/j.crma.2007.01.022
%G en
%F CRMATH_2007__344_6_395_0
Jia, Guangyan; Peng, Shige. On the set of solutions of a BSDE with continuous coefficient. Comptes Rendus. Mathématique, Tome 344 (2007) no. 6, pp. 395-397. doi : 10.1016/j.crma.2007.01.022. http://www.numdam.org/articles/10.1016/j.crma.2007.01.022/

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

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

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

[4] Pardoux, E.; Peng, S. 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.