03-165 Martin Hairer
Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion (450K, PDF) 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.

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