We study the ergodic properties of finite-dimensional systems of SDEs driven
by non-degenerate additive fractional Brownian motion with arbitrary Hurst
parameter H∈(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 SDE
possesses a unique stationary solution and that the convergence rate of an
arbitrary solution towards the stationary one is (at least) algebraic. A lower
bound on the exponent is also given.Comment: 49 pages, 8 figure