Abstract
Let µe be invariant measures of the Markov chains xnf which are small random perturbations of an endomorphism f of the interval [0, 1] satisfying the conditions of Misiurewicz [6]. It is shown here that in the ergodic case µe converges as ε 0 to the smooth f-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.
Original language | English |
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Title of host publication | Volume 1 |
Subtitle of host publication | The Collected Works of Anatole Katok |
Publisher | World Scientific Publishing Co. |
Pages | 215-259 |
Number of pages | 45 |
ISBN (Electronic) | 9789811237768 |
ISBN (Print) | 9789811237751 |
State | Published - 1 Jan 2024 |
Bibliographical note
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