Abstract
We 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.
Original language | English |
---|---|
Pages (from-to) | 431-456 |
Number of pages | 26 |
Journal | Bernoulli |
Volume | 12 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2006 |
Keywords
- Fractional Brownian motion
- Fractional Ornstein-Uhlenbeck process
- Fractional Vasicek model
- Fractional integral
- Langevin equation
- Long-range dependence
- Riemann-Stieltjes integrals
- Solution of stochastic differential equations
- State space transform
- Stochastic calculus