Abstract
Let μe be invariant measures of the Markov chainsx n F which are small random perturbations of an endomorphismf of the interval [0,1] satisfying the conditions of Misiurewicz [6]. It is shown here that in the ergodic case μe converges as e→0 to the smoothf-invariant measure which exists according to [6]. This result exhibits the first example of stability with respect to random perturbations while stability with respect to deterministic perturbations does not take place.
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