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Non-Markovian invariant measures are hyperbolic

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  • Crauel, Hans

Abstract

Suppose [mu] is an invariant measure for a smooth random dynamical system on a d-dimensional Riemannian manifold. We prove that [alpha][mu][less-than-or-equals, slant]dE[mu](max{0,-[lambda][mu]d}), where [alpha][mu] is the relative entropy of [mu], [lambda][mu]d is thesmallest Lyapunov exponent associated with [mu], and E[mu] denotes integration with respect to [mu].

Suggested Citation

  • Crauel, Hans, 1993. "Non-Markovian invariant measures are hyperbolic," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 13-28, March.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:1:p:13-28
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    Cited by:

    1. Cohen, Serge & Panloup, Fabien, 2011. "Approximation of stationary solutions of Gaussian driven stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2776-2801.
    2. Cohen, Serge & Panloup, Fabien & Tindel, Samy, 2014. "Approximation of stationary solutions to SDEs driven by multiplicative fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1197-1225.

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