Comptes Rendus
no. 9
Probability Theory
A type of time-symmetric forward–backward stochastic differential equations
[Un type d'équations différentielles stochastiques progressives–rétrogrades symétriques par rapport au temps]

Présenté par : Paul Malliavin

Shige Peng1 ; Yufeng Shi1 
1 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 773-778.

Nous étudions dans cette Note un type d'équations différentielles stochastiques progressives–rétrogrades symétriques par rapport au temps. Sous certaines conditions de monotonie, nous donnons un théorème d'existence et unicité des solutions des équations par une méthode de continuation. Ensuite nous présentons une application.

In this Note, we study a type of time-symmetric forward–backward stochastic differential equations. Under some monotonicity assumptions, we establish the existence and uniqueness theorem by means of a method of continuation. We also give an application.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00183-3
Shige Peng 1 ; Yufeng Shi 1

1 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China 
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Shige Peng; Yufeng Shi. A type of time-symmetric forward–backward stochastic differential equations. Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 773-778. doi : 10.1016/S1631-073X(03)00183-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00183-3/

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[4] N. El Karoui; S. Peng; M.-C. Quenez Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997), pp. 1-71

[5] Y. Hu; S. Peng Solution of forward–backward stochastic differential equations, Probab. Theory Related Fields, Volume 103 (1995), pp. 273-283

[6] J. Ma; P. Protter; J. Yong Solving forward–backward stochastic differential equations explicitly – a four step scheme, Probab. Theory Related Fields, Volume 98 (1994), pp. 339-359

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

[8] E. Pardoux; S. Peng Backward doubly stochastic differential equations and systems of quasilinear parabolic SPDE's, Probab. Theory Related Fields, Volume 98 (1994), pp. 209-227

[9] S. Peng Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics, Volume 37 (1991), pp. 61-74

[10] S. Peng Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions, Stochastic Process. Appl., Volume 88 (2000), pp. 259-290

[11] S. Peng; Y. Shi Infinite horizon forward–backward stochastic differential equations, Stochastic Process. Appl., Volume 85 (2000), pp. 75-92

[12] S. Peng; Z. Wu Fully coupled forward–backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., Volume 37 (1999), pp. 825-843

[13] J. Yong Finding adapted solutions of forward–backward stochastic differential equations – method of continuation, Probab. Theory Related Fields, Volume 107 (1997), pp. 537-572

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