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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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      Author and article information

      Journal
      10 April 2003
      2004-03-09
      math/0304134
      Custom metadata
      60H10; 60G10; 37H10
      49 pages, 8 figures
      math.PR

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