Geodesic
Probability Theory
A uniqueness theorem for the solution of Backward Stochastic Differential Equations
[Un théorême d'unicité de la solution d'une équation différentielle stochastique rétrograde]

Présenté par : Marc Yor

Jia, Guangyan1
1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, PR China
Comptes Rendus. Mathématique, Tome 346 (2008) no. 7-8, pp. 439-444.

Voir la notice de l'article provenant de la source Numdam

In this Note, we prove that if g is uniformly continuous in z, uniformly with respect to (ω,t) and independent of y, the solution to the backward stochastic differential equation (BSDE) with generator g, is unique.

Dans cette Note, nous démontrons que pour une fonction g donnée, uniformément continue en z, uniformément en (ω,t) et indépendante de y l'équation différentielle stochastique, rétrograde de générateur g, admet une solution unique.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.02.012

Jia, Guangyan 1

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, PR China 
@article{CRMATH_2008__346_7-8_439_0,
     author = {Jia, Guangyan},
     title = {A uniqueness theorem for the solution of {Backward} {Stochastic} {Differential} {Equations}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {439--444},
     publisher = {Elsevier},
     volume = {346},
     number = {7-8},
     year = {2008},
     doi = {10.1016/j.crma.2008.02.012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2008.02.012/}
}
TY  - JOUR
AU  - Jia, Guangyan
TI  - A uniqueness theorem for the solution of Backward Stochastic Differential Equations
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 439
EP  - 444
VL  - 346
IS  - 7-8
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2008.02.012/
DO  - 10.1016/j.crma.2008.02.012
LA  - en
ID  - CRMATH_2008__346_7-8_439_0
ER  - 
%0 Journal Article
%A Jia, Guangyan
%T A uniqueness theorem for the solution of Backward Stochastic Differential Equations
%J Comptes Rendus. Mathématique
%D 2008
%P 439-444
%V 346
%N 7-8
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2008.02.012/
%R 10.1016/j.crma.2008.02.012
%G en
%F CRMATH_2008__346_7-8_439_0
Jia, Guangyan. A uniqueness theorem for the solution of Backward Stochastic Differential Equations. Comptes Rendus. Mathématique, Tome 346 (2008) no. 7-8, pp. 439-444. doi : 10.1016/j.crma.2008.02.012. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2008.02.012/

[1] Briand, P.; Hu, Y. Quadratic BSDEs with convex generators and unbounded terminal conditions, 2007 (available in arXiv:) | arXiv

[2] Coquet, F.; Hu, Y.; Mémin, J.; Peng, S. Filtration consistent nonlinear expectations and related g-expectations, Probab. Theory Related Fields, Volume 123 (2002), pp. 1-27

[3] Crandall, M.G. Viscosity solutions—a primer (Capuzzo Dolcetta, I.; Lions, P.L., eds.), Viscosity Solutions and Applications, Lecture Notes in Mathematics, vol. 1660, Springer, Berlin, 1997, pp. 1-43

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

[5] Lepeltier, J.P.; San Martin, J. Backward stochastic differential equations with continuous coefficients, Statist. Probab. Lett., Volume 32 (1997) no. 4, pp. 425-430

[6] Pardoux, E. Backward stochastic differential equations and viscosity solutions of system of semilinear parabolic and elliptic PDEs of second order, Stochastic Analysis and Related Topics, VI, Birkhäuser, 1996, pp. 79-128

[7] Pardoux, E.; Peng, S. Adapted solutions of a backward stochastic differential equations, System Control Lett., Volume 14 (1990) no. 1, pp. 55-61

[8] E. Pardoux, S. Peng, Some backward SDEs with non-Lipschitz, coefficients, Prepublication URA 225, 94-3, Universite de Provence

Cité par Sources :