Nonstandard central limit theorems for Markov chains

Bernardo B. De Andrade, Charles J. Geyer

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Abstract

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 Knowlege-Based Systems
Volume19
Issue number2
DOIs
StatePublished - Apr 1 2011

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Keywords

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

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