Solutions to BSDEs Driven by Both Standard and Fractional Brownian Motions  

作　　者：Wei-yin FEI Deng-Feng XIA Shu-guang ZHANG 

机构地区：[1]Department of Applied Mathematics, Anhui Polytechnic University [2]Department of Statistics and Finance, University of Science and Technology of China

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第2期329-354,共26页应用数学学报（英文版）

基　　金：Supported by National Basic Research Program of China (973 Program, No. 2007CB814901);National Natural Science Foundation of China (No. 71171003);Anhui Natural Science Foundation (No. 090416225);Anhui Natural Science Foundation of Universities (No. KJ2010A037)

摘　　要：The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 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.The backward stochastic differential equations driven by both standard and fractional Brownian motions （or, in short, SFBSDE） axe studied. A Wick-It6 stochastic integral for a fractional Brownian motion is adopted. The fractional It6 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.

关 键 词：fractional Brownian motion Malliavin calculus fractional It6 formula quasi-conditional expec-tation SFBSDE 

分 类 号：O175[理学—数学]