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Ergodic theory for SDEs with extrinsic memory. (English) Zbl 1129.60052
From the authors’ summary: We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topolgical irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas’minskii theorem.
The second part of this article shows how it is possible to apply these results to the case of stochastic differential equations driven by fractional Brownian motion. It follows that under a nondegeneracy condition on the noise, such equations admit a unique adapted stationary solution.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G10 Stationary stochastic processes
26A33 Fractional derivatives and integrals
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