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Strong stochastic stability and rate of mixing for unimodal maps. (English) Zbl 0868.58051
Let \(I\) be a compact real interval and \(f: I\to I\) be a unimodal map with negative Schwarzian derivative and nondegenerate critical point. Then under certain further assumptions the authors show that these maps are stable under random perturbations of the map – in the sense of \(L_1\) convergence of invariant densities of the associated Markov chain (strong stochastic stability). The authors also give uniform bounds for the exponential rate of decay of correlations.
Reviewer: R.Cowen (Gaborone)

MSC:
37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
37A25 Ergodicity, mixing, rates of mixing
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
37H99 Random dynamical systems
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