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On the normal approximation for random fields via martingale methods

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  • Peligrad, Magda
  • Zhang, Na

Abstract

We prove a central limit theorem for strictly stationary random fields under a sharp projective condition. The assumption was introduced in the setting of random sequences by Maxwell and Woodroofe. Our approach is based on new results for triangular arrays of martingale differences, which have interest in themselves. We provide as applications new results for linear random fields and nonlinear random fields of Volterra-type.

Suggested Citation

  • Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1333-1346
    DOI: 10.1016/j.spa.2017.07.012
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    References listed on IDEAS

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    1. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    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.
    2. Davydov, Youri & Tempelman, Arkady, 2024. "Randomized limit theorems for stationary ergodic random processes and fields," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    3. 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.
    4. Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.

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