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Almost-Sure Results for a Class of Dependent Random Variables

Author

Listed:
  • Magda Peligrad

    (University of Cincinnati)

  • Allan Gut

    (Uppsala University)

Abstract

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by ℤ d + —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:1:d:10.1023_a:1021744626773
    DOI: 10.1023/A:1021744626773
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    References listed on IDEAS

    as
    1. Paranjape, S. R. & Park, C., 1973. "Laws of iterated logarithm of multiparameter wiener processes," Journal of Multivariate Analysis, Elsevier, vol. 3(1), pages 132-136, March.
    2. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.
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    Cited by:

    1. Richard C. Bradley, 2001. "A Stationary Rho-Mixing Markov Chain Which Is Not “Interlaced” Rho-Mixing," Journal of Theoretical Probability, Springer, vol. 14(3), pages 717-727, July.
    2. 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.
    3. Feng, Fengxiang, 2023. "Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums under sub-linear expectations," Statistics & Probability Letters, Elsevier, vol. 197(C).
    4. 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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