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On the functional CLT for stationary Markov chains started at a point

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  • Barrera, David
  • Peligrad, Costel
  • Peligrad, Magda

Abstract

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy this type of asymptotic result. One of the theorems shows that if a Markov chain is stationary ergodic and reversible, this result holds for bounded additive functionals of the chain which have a martingale coboundary in L1 representation. Our results are also well adapted for strongly mixing sequences providing for this case an alternative, shorter approach to some recent results in the literature.

Suggested Citation

  • Barrera, David & Peligrad, Costel & Peligrad, Magda, 2016. "On the functional CLT for stationary Markov chains started at a point," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1885-1900.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:7:p:1885-1900
    DOI: 10.1016/j.spa.2015.12.001
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    References listed on IDEAS

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    1. Dehling, Herold & Durieu, Olivier & Volny, Dalibor, 2009. "New techniques for empirical processes of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3699-3718, October.
    2. Volný, Dalibor & Woodroofe, Michael, 2014. "Quenched central limit theorems for sums of stationary processes," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 161-167.
    3. Rassoul-Agha, F. & Seppäläinen, T., 2008. "An almost sure invariance principle for additive functionals of Markov chains," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 854-860, May.
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    Cited by:

    1. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.

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