Deconvolution of fractional brownian motion

We show that a fractional Brownian motion with H'∈(0,1) can be represented as an explicit transformation of a fractional Brownian motion with index H ∈(0,1). In particular, when H'=½, we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion. We work both in the `time domain' and the `spectral domain' and contrast the advantages of one domain over the other.