A uniqueness theorem for the solution of Backward Stochastic Differential Equations

Guangyan Jia

doi:10.1016/j.crma.2008.02.012

Probability Theory

A uniqueness theorem for the solution of Backward Stochastic Differential Equations

Presented by: Marc Yor

Guangyan Jia ¹

¹ School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, PR China

Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 439-444.

Abstract
Résumé

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.

Received: 2007-04-11
Accepted: 2008-02-12
Published online: 2008-03-24

DOI: 10.1016/j.crma.2008.02.012

Author's affiliations:

Guangyan Jia ¹

¹ School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, PR China

@article{CRMATH_2008__346_7-8_439_0,
     author = {Guangyan Jia},
     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},
}

TY  - JOUR
AU  - Guangyan Jia
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
DO  - 10.1016/j.crma.2008.02.012
LA  - en
ID  - CRMATH_2008__346_7-8_439_0
ER  -

%0 Journal Article
%A Guangyan Jia
%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
%R 10.1016/j.crma.2008.02.012
%G en
%F CRMATH_2008__346_7-8_439_0

Guangyan Jia. A uniqueness theorem for the solution of Backward Stochastic Differential Equations. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 439-444. doi : 10.1016/j.crma.2008.02.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.012/

References
Cited by

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

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

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

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

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

[6] E. Pardoux 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] E. Pardoux; S. Peng 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

Cited by Sources:

Comments - Policy