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The invariance principle for linear multi-parameter stochastic processes generated by associated fields

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  • Kim, Tae-Sung
  • Ko, Mi-Hwa
  • Choi, Yong-Kab

Abstract

We derive the invariance principle for the linear random field generated by identically distributed and associated random fields. Our result extends the result in Bulinski and Keane [Bulinski, A.V., Keane, M.S., 1996. Invariance principle for associated random fields. J. Math. Sci. 81, 2905-2911.] to the linear random field in the identically distributed case as well as the result in Marinucci and Poghosyan [Marinucci, M., Poghosyan, S., 2001. Asymptotics for linear random fields. Probab. Lett. 51, 131-141.] to the associated case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3298-3303
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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.
    2. Marinucci, D. & Poghosyan, S., 2001. "Asymptotics for linear random fields," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 131-141, January.
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