Conditional expectations of a fractional Brownian motion with
Hurst index H respect to the filtration of a fractional Brownian motion with Hurst index L, both contained in the fractional Brownian field, are studied. As processes, the conditional expectations contain martingale components and for dual pairs of Hurst indices, H+L=1, they become pure martingales. A stochastic integral representation of those processes is constructed directly from the covariance structure of the underlying fractional Brownian field.
The talk presents a joint work with Francisco Ojeda.