Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

Martin Hairer

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Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

Martin Hairer

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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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BibTeX RIS

Martin Hairer. 2004-03-09. Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion. https://arxiv.org/abs/math/0304134

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