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# 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.

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###### Journal
10 April 2003
2004-03-09
math/0304134