Probability Theory
On the set of solutions of a BSDE with continuous coefficient
Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 395-397.

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.

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.

Received:
Accepted:
Published online:
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
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Jia, Guangyan; Peng, Shige. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.01.022/

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[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

Cited by Sources:

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