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Asymptotics for linear random fields

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  • Marinucci, D.
  • Poghosyan, S.

Abstract

We prove that partial sums of linear multiparameter stochastic processes can be represented as partial sums of independent innovations plus components that are uniformly of smaller order. This representation is exploited to establish functional central limit theorems and strong approximations for random fields.

Suggested Citation

  • Marinucci, D. & Poghosyan, S., 2001. "Asymptotics for linear random fields," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 131-141, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:2:p:131-141
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    References listed on IDEAS

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    1. Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
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    Cited by:

    1. Paulauskas, Vygantas, 2010. "On Beveridge-Nelson decomposition and limit theorems for linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 621-639, March.
    2. 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.
    3. Banys, Povilas & Davydov, Youri & Paulauskas, Vygantas, 2010. "Remarks on the SLLN for linear random fields," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 489-496, March.

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