BACKWARD STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

被引：54
作者：
Hu, Yaozhong [1 ]
Peng, Shige [2 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[2] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 48卷 / 03期
基金：
美国国家科学基金会;
关键词：
backward stochastic differential equation; fractional Brownian motion; quasi-conditional expectation; CALCULUS; NOISE; FINANCE;
D O I：
10.1137/070709451
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We study general linear and nonlinear backward stochastic differential equations driven by fractional Brownian motions. The existence and uniqueness of the solutions are obtained under some mild assumptions. In the nonlinear case we obtain an inequality of the type similar to in the classical backward stochastic differential equations. This leads to a fixed point principle. An important tool is the quasi-conditional expectation introduced in [Y. Hu and B. Oksendal, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6 (2003), pp. 1-32]. We also give a detailed study on this new "expectation."
引用
收藏
页码：1675 / 1700
页数：26
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