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Limit theorems for weighted Bernoulli random fields under Hannan’s condition

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  • Klicnarová, Jana
  • Volný, Dalibor
  • Wang, Yizao

Abstract

Recently, invariance principles for partial sums of Bernoulli random fields over rectangular index sets have been proved under Hannan’s condition. In this note we complement previous results by establishing limit theorems for weighted Bernoulli random fields, including central limit theorems for partial sums over arbitrary index sets and invariance principles for Gaussian random fields. Most results improve earlier ones on Bernoulli random fields under Wu’s condition, which is stronger than Hannan’s condition.

Suggested Citation

  • Klicnarová, Jana & Volný, Dalibor & Wang, Yizao, 2016. "Limit theorems for weighted Bernoulli random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1819-1838.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:6:p:1819-1838
    DOI: 10.1016/j.spa.2015.12.006
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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. Truquet, Lionel, 2010. "A moment inequality of the Marcinkiewicz-Zygmund type for some weakly dependent random fields," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1673-1679, November.
    3. Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
    4. 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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    1. Giraudo, Davide, 2024. "Deviation inequality for Banach-valued orthomartingales," Stochastic Processes and their Applications, Elsevier, vol. 175(C).

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