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Convergence of series of conditional expectations

Author

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  • Peligrad, M.
  • Peligrad, C.

Abstract

This paper deals with almost sure convergence for partial sums of Banach space valued random variables. The results are then applied to solve similar problems for weighted partial sums of conditional expectations. They are further used to treat partial sums of powers of a reversible Markov chain operator. The method of proof is based on martingale approximation. The conditions are expressed in terms of moments of individual summands.

Suggested Citation

  • Peligrad, M. & Peligrad, C., 2023. "Convergence of series of conditional expectations," Statistics & Probability Letters, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:stapro:v:200:y:2023:i:c:s0167715223000937
    DOI: 10.1016/j.spl.2023.109869
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    Cited by:

    1. 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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