Fractional integral equations and state space transforms
We introduce a class of stochastic differential equations driven by fractional Brownian motion (FBM), which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extention of fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated. Their stationary densities are given explicitly.
Fractional Brownian motion, fractional integral, fractional Ornstein- Uhlenbeck process, fractional Vasicek model, Langevin equation, long range dependence, Riemann-Stieltjes integrals, state space transform, stochastic calculus, solution of SDE