When a fractional brownian motion has a Hurst exponent < 0.5, it corresponds to a mean reverting process. Are there values of the parameters of a fractional brownian motion and an Ornstein-Uhlenbeck process for which they correspond to the exact same stochastic process?
Or are there fundamental differences between a mean reverting fractional brownian motion and an ornstein-uhlenbeck process, such that they can't be made equivalent?