Ergodicity of stochastic differential equations driven by fractional Brownian motion

We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H is an element of (0, 1). A general framework is constructed to make precise the notions of "invariant measure" and "stationary state" for such a system. We then prove under rather weak dissipativity conditions that such an SIDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the stationary one is (at least) algebraic. A lower bound on the exponent is also given.