Journal of Theoretical Probability

, Volume 8, Issue 3, pp 549–570 | Cite as

Uniform CLT for Markov chains and its invariance principle: A martingale approach

  • Jongsig Bae
  • Shlomo Levental


The convergence of stochastic processes indexed by parameters which are elements of a metric space is investigated in the context of an invariance principle of the uniform central limit theorem (UCLT) for stationary Markov chains. We assume the integrability condition on metric entropy with bracketing. An eventual uniform equicontinuity result is developed which essentially gives the invariance principle of the UCLT. We translate the problem into that of a martingale difference sequence as in Gordin and Lifsic.(7) Then we use the chaining argument with stratification adapted from that of Ossiander.(11) The results of this paper generalize those of Levental(10) and Ossiander.(11)

Key Words

Markov chains invariance principle uniform central limit theorem martingales 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Jongsig Bae
    • 1
  • Shlomo Levental
    • 1
  1. 1.Department of Statistics and ProbabilityMichigan State UniversityEast Lansing

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