Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

Details Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

2003-04-10

arxiv.org/abs/math/0304134v2

Mathematics

Probability

49 pages, 8 figures

Scientific paper

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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