Solutions to BSDEs Driven by Both Standard and Fractional Brownian Motions

被引：0

作者：

Wei-yin FEI ^{[1
]}

Deng-Feng XIA ^{[1
]}

Shu-guang ZHANG ^{[2
]}

机构：

[1] Department of Applied Mathematics, Anhui Polytechnic University

[2] Department of Statistics and Finance, University of Science and Technology of China

来源：

Acta Mathematicae Applicatae Sinica | 2013年 / 02期

基金：

安徽省自然科学基金; 中国国家自然科学基金;

关键词：

fractional Brownian motion; Malliavin calculus; fractional Ito formula; quasi-conditional expec- tation; SFBSDE;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

The backward stochastic differential equations driven by both standard and fractional Brownian motions (or, in short, SFBSDE) are studied. A Wick-It? stochastic integral for a fractional Brownian motion is adopted. The fractional It? formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.

引用

页码：329 / 354

页数：26

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