Buchmann, BorisKlueppelberg, Claudia C2015-12-071350-7265http://hdl.handle.net/1885/24366We introduce a class of stochastic differential equations driven by fractional Brownian motion which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extension of the fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated, and their stationary densities are explicitly given.Keywords: Fractional Brownian motion; Fractional integral; Fractional Ornstein-Uhlenbeck process; Fractional Vasicek model; Langevin equation; Long-range dependence; Riemann-Stieltjes integrals; Solution of stochastic differential equations; State space transform;200610.3150/bj/11515251292015-12-07