On Gaussian processes equivalent in law to fractional Brownian motion (Q1827446)

This paper considers Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. The paper proves a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index \(H\leq \frac{1}{2}\). For the case \(H>\frac{1}{2}\) it is shown that such a representation cannot hold. The paper also considers briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation the paper considers a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise.