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Central Limit Theorem for some non-stationary Markov chains

Volume 246 / 2019

Jacek Gulgowski, Sander Hille, Tomasz Szarek, Maria Ziemlańska Studia Mathematica 246 (2019), 109-131 MSC: Primary 60F05, 60J05; Secondary 37A25, 37A30. DOI: 10.4064/sm170325-8-9 Published online: 24 September 2018

Abstract

Using the classical Central Limit Theorem for stationary Markov chains proved by M. I. Gordin and B. A. Lifshits (1978) we show that it also holds for non-stationary Markov chains provided the transition probabilities satisfy the spectral gap property in the Kantorovich–Rubinstein norm.

Authors

  • Jacek GulgowskiInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Sander HilleMathematical Institute
    Leiden University
    P.O. Box 9512
    2300 RA Leiden, The Netherlands
    e-mail
  • Tomasz SzarekInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail
  • Maria ZiemlańskaMathematical Institute
    Leiden University
    P.O. Box 9512
    2300 RA Leiden, The Netherlands
    e-mail

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