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A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

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Abstract

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly \(\alpha \)-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Rawles Hall 313, Bloomington, IN, 47405, USA

    Richard C. Bradley

  2. Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY, 40292, USA

    Cristina Tone

Authors
  1. Richard C. Bradley
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  2. Cristina Tone
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Corresponding author

Correspondence to Cristina Tone.

Additional information

Cristina Tone is supported partially by the NSA Grant H98230-15-1-0006.

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Bradley, R.C., Tone, C. A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields. J Theor Probab 30, 655–674 (2017). https://doi.org/10.1007/s10959-015-0656-2

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  • DOI: https://doi.org/10.1007/s10959-015-0656-2

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