Random perturbations of transformations of an interval

A. Katok, Y. Kifer

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Let με be invariant measures of the Markov chains x n F 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 με 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 (US)
Pages (from-to)193-237
Number of pages45
JournalJournal d'Analyse Mathématique
Volume47
Issue number1
DOIs
StatePublished - Dec 1 1986

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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