Weak solutions and a Yamada-Watanabe theorem for FBSDEs

被引：8

作者：

Bahlali, K. ^{[1
]}

Mezerdi, B. ^{[2
]}

N'zi, M. ^{[3
]}

Ouknine, Y. ^{[4
]}

机构：

[1] UVT, UFR Sci, BP 132, F-83957 La Garde, France

[2] Univ Mohamed Khider, Dept Math, Lab Math Appl, Biskra, Algeria

[3] Univ Adidjan, UFR Math & Informat, Abidjan, Cote Ivoire

[4] Univ Cadi Ayyad, Fac Sci Semlalia, Dept Math, Marrakech 40000, Morocco

来源：

RANDOM OPERATORS AND STOCHASTIC EQUATIONS | 2007年 / 15卷 / 03期

关键词：

Forward-backward stochastic differential equation; weak solution; YamadaWatanabe theorem; Girsanov theorem; Burgers equation;

D O I：

10.1515/ROSE.2007.016

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a Yamada-Watanabe theorem for forward-backward stochastic differential equations (FBSDEs). As a consequence, we show that weak existence and pathwise uniqueness of the solution imply the existence of a strong solution. We use this result to establish existence and uniqueness of weak solutions for a large class of FBSDEs. We also give a probabilistic interpretation of the solutions of certain nonlinear partial differential equations (PDEs).

引用

页码：271 / 285

页数：15

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