Integral representation with adapted continuous integrand with respect   to fractional Brownian motion
  We show that if a random variable is a final value of an adapted Holder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian motion, and the integrand is an adapted process, continuous up to the final point. 
Georgiy Shevchenko and Lauri Viitasaari
math.PR