Properties of solution of fractional backward stochastic differential equation

The backward stochastic differential equations (BSDEs) driven by fractional Brownian motion are studied. As an important tool, the quasi-conditional expectation is used. The general forms of Jensen's inequality of quasi-conditional expectation are proved. For the linear BSDEs, their solutions are represented by using the quasi-conditional expectation. Moreover, the comparison theorem and comonotonic theorem of the solutions of linear BSDEs are derived.