Forward-backward stochastic differential equations with nonsmooth coefficients

被引：13

作者：

Hu, Y

Yong, JM

机构：

[1] Univ Rennes 1, CNRS, UMR 6625, IRMAR, F-35042 Rennes, France

[2] Fudan Univ, Dept Math, Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Inst Math Finance, Shanghai 200433, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 87卷 / 01期

关键词：

forward-backward stochastic differential equation; four-step scheme; nonlinear Feynman-Kac formula; viscosity solution;

D O I：

10.1016/S0304-4149(99)00106-4

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：

Solvability of forward-backward stochastic differential equations with nonsmooth coefficients is considered using the Four-Step Scheme and some approximation arguments. For the one-dimensional case, the existence of an adapted solution is established for the equation which allows the diffusion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution to a one-dimensional nonsmooth degenerate quasilinear parabolic partial differential equation. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：93 / 106

页数：14

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