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Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion. (English) Zbl 1180.93095
Summary: We study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases.

MSC:
93E03 Stochastic systems in control theory (general)
93B18 Linearizations
93E12 Identification in stochastic control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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