ar 2 00 4 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 1 , 2008

@inproceedings{Hairer2003ar20,
  title={ar 2 00 4 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 1 , 2008},
  author={Martin Hairer},
  year={2003}
}
We study the ergodic properties of finite-dimensional syste m of SDEs driven by non-degenerate additive fractional Brownian motion with a rbitrary Hurst parameter H ∈ (0, 1). A general framework is constructed to make precise the not io s of “invariant measure” and “stationary state” for such a syste m. We then prove under rather weak dissipativity conditions that such an SDE posse sses a unique stationary solution and that the convergence rate of an arbitrary solut ion towards the stationary… CONTINUE READING