- 03-165 Martin Hairer
- Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion
Apr 10, 03
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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.