Abstract
A position dependent random map is a dynamical system consisting of a collection of maps such that, at each iteration, a selection of a map is made randomly by means of probabilities which are functions of position. Let f* be an invariant density of the position dependent random map T. We consider a model of small random perturbations 𝔗ϵ of the random map T. For each ϵ > 0, 𝔗ϵ has an invariant density function f ϵ. We prove that f ϵ → f* as ϵ → 0.
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