Random Perturbations of Transformations of an Interval

A. Katok, Y. Kifer

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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 languageEnglish
Title of host publicationVolume 1
Subtitle of host publicationThe Collected Works of Anatole Katok
PublisherWorld Scientific Publishing Co.
Pages215-259
Number of pages45
ISBN (Electronic)9789811237768
ISBN (Print)9789811237751
StatePublished - 1 Jan 2024

Bibliographical note

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© 2024 by World Scientific Publishing Co. Pte. Ltd.

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