Hairer, MartinPillai, N. S.2024-09-172024-09-172024-09-112011-05-0110.1214/10-AIHP377https://infoscience.epfl.ch/handle/20.500.14299/241209WOS:000289654500013We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1/2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hormander'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.enDIFFERENTIAL-EQUATIONS DRIVENMALLIAVIN CALCULUSErgodicityFractional Brownian motionHormander's theoremScience & TechnologyPhysical Sciencestext::journal::journal article