RANDOM PERTURBATIONS OF TRANSFORMATIONS OF AN INTERVAL

A. Katok; Y. Kifer

RANDOM PERTURBATIONS OF TRANSFORMATIONS OF AN INTERVAL

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Let µ r be invariant measures of the Markov chains x_m^r which are small random perturbations of an endomorphism f of the interval [0, l J satisfying the conditions of Misiurewicz [6). It is shown here that in the ergodic case µ 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
Title of host publication	The Collected Works of Anatole Katok
Subtitle of host publication	In 2 Volumes
Publisher	World Scientific Publishing Co.
Pages	215-259
Number of pages	45
Volume	2
ISBN (Electronic)	9789811238079
ISBN (Print)	9789811238062
State	Published - 1 Jan 2024

Bibliographical note

Publisher Copyright:
© 1986 Springer Nature.

Cite this

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RANDOM PERTURBATIONS OF TRANSFORMATIONS OF AN INTERVAL

Abstract

Bibliographical note

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