Transformation formulas for fractional Brownian motion

We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H . Integration is carried out over [ 0 , t ] , t > 0 . The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L 2 ( P ) -sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over ( − ∞ , t ] , t > 0 .