Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

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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.
49 pages, 8 figures

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Probability, 60H10; 60G10; 37H10

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http://salesiana.dossiersoluciones.com/handle/123456789/67039

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304134
 http://arxiv.org/abs/math/0304134

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arXiv