Nonstandard central limit theorems for Markov chains

Bernardo B. De Andrade, Charles J. Geyer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove a nonstandard central limit theorem for strongly mixing stationary sequences using the "radically elementary" probability theory developed by Nelson (1987) and use this result to obtain a nonstandard Markov chain central limit theorem. An analogue of a Gaussian autoregressive process is used to illustrate how to obtain the rate of convergence. A Markov chain nonstandard functional central limit theorem is also proved under conditions similar to square integrability of the underlying martingale.

Original languageEnglish (US)
Pages (from-to)251-274
Number of pages24
JournalInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Issue number2
StatePublished - Apr 2011

Bibliographical note

Funding Information:
The first author would like to thank FINATEC/UNB (Grant Fomento-4/09) for the partial support given during his stay at the Department of Economics, University of Brasília, while this work was being completed.


  • Central limit theorem
  • Markov chains
  • functional CLT
  • nonstandard analysis


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