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 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.展开更多
基金Supported by National Basic Research Program of China (973 Program, No. 2007CB814901)National Natural Science Foundation of China (No. 71171003)+1 种基金Anhui Natural Science Foundation (No. 090416225)Anhui Natural Science Foundation of Universities (No. KJ2010A037)
文摘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.
