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On limit theorems for fields of martingale differences

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  • Volný, Dalibor

Abstract

We prove a central limit theorem for stationary multiple (random) fields of martingale differences f∘Ti̲, i̲∈Zd, where Ti̲ is a Zd action. In most cases the multiple (random) fields of martingale differences is given by a completely commuting filtration. A central limit theorem proving convergence to a normal law has been known for Bernoulli random fields and in Volný (2015) this result was extended to random fields where one of generating transformations is ergodic.

Suggested Citation

  • Volný, Dalibor, 2019. "On limit theorems for fields of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 841-859.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:841-859
    DOI: 10.1016/j.spa.2018.03.021
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    References listed on IDEAS

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    1. Giraudo, Davide & Volný, Dalibor, 2014. "A strictly stationary β-mixing process satisfying the central limit theorem but not the weak invariance principle," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3769-3781.
    2. Volný, Dalibor & Wang, Yizao, 2014. "An invariance principle for stationary random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4012-4029.
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    Cited by:

    1. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.

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