Functional central limit theorems for iterated function systems controlled by regenerative sequences

O. Lee, D. W. Shin

Research output: Contribution to journalArticlepeer-review

Abstract

Let X be a Polish space and let S be a measurable space. Let {In} be a regenerative process with state space s. Take Z0 arbitrary but independent of {In}. We consider an iterated function system obtained recursively by Zn = FIn-1 (Zn-1)(n ≥ 1), where the function F : X × S → X defined by F(x, s) = Fs (x) is measurable and for each s ∈ S, Fs (x) is a continuous function of x. We obtain sufficient conditions under which, whatever the initial distribution, the functional central limit theorem holds.

Original languageEnglish
Pages (from-to)1749-1759
Number of pages11
JournalIndian Journal of Pure and Applied Mathematics
Volume32
Issue number11
StatePublished - Nov 2001

Keywords

  • Functional central limit theorem
  • Invariant probability
  • Markov chain
  • Regenerative process

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