Fractional Hida Malliavin Derivatives and Series Representations of   Fractional Conditional Expectations
  We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we obtain a backward Taylor series representation; when the target functional is generated by a continuous fractional filtration, the series representation is obtained by applying a "frozen path" operator and an exponential operator to the functional. Three examples are provided to show that our representation gives useful series expansions of ordinary expectations of target random variables. 
Sixian Jin, Qidi Peng and Henry Schellhorn
math.PR