## Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion.(English. French summary)Zbl 1221.60083

From the authors’ abstract: We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter $$H>\frac12$$ have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical in the sense that it does not “look into the future.”
The main technical result required for the analysis is a bound on the moments of the inverse of the Malliavin covariance matrix, conditional on the past of the driving noise.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G10 Stationary stochastic processes 60H07 Stochastic calculus of variations and the Malliavin calculus 26A33 Fractional derivatives and integrals
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### References:

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