Limit laws for ergodic processes

Jean Paul Thouvenot*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The study of limit laws for normalized sums of a sequence of random variables is one of the classical topics in probability theory. We give here two results showing that ergodic stationary processes can admit an arbitrary distribution as the limit of normalized sums. In the first, we take the usual average of the first n variables, but the process is not integrable. In the second, the variables take on only two values and the sequence of normalizing constants is constructed inductively. In both cases the processes can be defined as factors of an arbitrary aperiodic measure preserving system.

Original languageEnglish
Article number1150012
JournalStochastics and Dynamics
Volume12
Issue number1
DOIs
StatePublished - Mar 2012

Keywords

  • ergodic processes
  • Limit laws

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