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Invariance principle for martingale-difference random fields

Author

Listed:
  • Poghosyan, S.
  • Roelly, S.

Abstract

A convergence criterium to the multi-parameter Wiener process is proved. Then, it is used to establish that a martingale-difference random field on the lattice satisfies an invariance principle.

Suggested Citation

  • Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
  • Handle: RePEc:eee:stapro:v:38:y:1998:i:3:p:235-245
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    Citations

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    Cited by:

    1. Baldi, Paolo & Kerkyacharian, Gérard & Marinucci, Domenico & Picard, Dominique, 2008. "High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 606-636, April.
    2. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    3. Marinucci, D. & Poghosyan, S., 2001. "Asymptotics for linear random fields," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 131-141, January.
    4. Nowak, Emmanuel & Thilly, Emmanuel, 2006. "A local invariance principle for Gibbsian fields," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1975-1982, December.
    5. 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.
    6. Kim, Tae-Sung & Ko, Mi-Hwa & Choi, Yong-Kab, 2008. "The invariance principle for linear multi-parameter stochastic processes generated by associated fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3298-3303, December.
    7. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    8. 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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