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Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables

Author

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  • Sergey Utev

    (University of Nottingham)

  • Magda Peligrad

    (University of Cincinnati)

Abstract

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle for strongly mixing sequences of random variables in the absence of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences.

Suggested Citation

  • Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:1:d:10.1023_a:1022278404634
    DOI: 10.1023/A:1022278404634
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    References listed on IDEAS

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    1. Peligrad, Magda, 1986. "Invariance principles under weak dependence," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 299-310, August.
    2. Bradley, Richard C. & Bryc, Wlodzimierz, 1985. "Multilinear forms and measures of dependence between random variables," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 335-367, June.
    3. Bradley, Richard C., 1981. "Central limit theorems under weak dependence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 1-16, March.
    4. Magda Peligrad & Allan Gut, 1999. "Almost-Sure Results for a Class of Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 12(1), pages 87-104, January.
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    Cited by:

    1. Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Dagmara Dudek & Anna Kuczmaszewska, 2024. "Some practical and theoretical issues related to the quantile estimators," Statistical Papers, Springer, vol. 65(6), pages 3917-3933, August.
    3. Leshun Xu & Alan Lee & Thomas Lumley, 2023. "A functional central limit theorem on non-stationary random fields with nested spatial structure," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 215-234, April.
    4. Li, Kunpeng, 2022. "Threshold spatial autoregressive model," MPRA Paper 113568, University Library of Munich, Germany.
    5. Richard C. Bradley & Cristina Tone, 2017. "A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields," Journal of Theoretical Probability, Springer, vol. 30(2), pages 655-674, June.
    6. Thành, Lê Vǎn, 2024. "On Rio’s proof of limit theorems for dependent random fields," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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