Martin Hairer
Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion
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ABSTRACT.  We study the ergodic properties of finite-dimensional systems of SDEs driven by 
non-degenerate additive fractional Brownian motion with 
arbitrary Hurst parameter $H\in(0,1)$. 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.